The Rate of Interest 0824053141

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Accountancy in Transition

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The Rate of Interest

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Irving Fisher with a new introduction by Donald Dewey

Garland Publishing, Inc. New York & London 1982

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This facsimile has been made from a copy in the New York Public Library. Introduction copyright © 1982 by Donald Dewey

Library of Congress Cataloging in Publication Data Fisher, Irving, 1867-1947. The rate of interest.

(Accountancy in transition) Reprint. Originally published: New York : Macmillan, 1907. Includes index 1. Interest and usury. I. Title. II. Series. HB539.F54 1982 332.8'2 82-48363 ISBN 0-8240-5314-1

The volumes in this series are printed on acid-free, 250-yearlife paper. Printed in the United States of America

Introduction Many economists who know the history of their subject believe that Irving Fisher (1867-1947) was their greatest colleague who lived and worked in the United States. Thus it is cause for near amazement that this bobok—the most original and fundamental of his twenty-nine—has been out of print for over sixty years. Fortunately for the reputation of economics, it was the genius of Fisher and not professional indifference that is largely responsible for this neglect. Today Fisher's best known work on capital and interest is The Theory of Interest (1930) which, without exaggeration, Joseph Schumpeter described as “a wonderful performance, the peak achievement, so far as perfection within its own frame is concerned, of the literature of interest./ Yet this book, written toward the end of Fisher's active professional life has little

claim to originality. It was intended by Fisher to gain a wider audience for his views and was, in fact, quarried from two books published many years before. Quite properly, given its pedagogical goal (brilliantly realized) The Theory of Interest excluded much and added little. For the complete Fisher on capital and interest one must go back to the earlier books. The first to appear was The Nature of Capital and Income (1906). Although still in print and much cited, it was essentially an

exercise in ground clearing and dealt mainly with problems of classifications, definition, and estimation. The ground having been cleared, one year later Fisher published The Rate of Inter-

est—the most original and, with the possible exception of J.M. Keynes’ The General Theory of Employment, Interest, and Money, the most influential book ever written in this controversial and confused area of economics. Before Fisher, the theory of capital and interest was, to put it charitably, in a state of serious dfsarray. Not only had econo-

mists achieved little success in explaining how interest rates are determined, they were not even able to answer with a single voice the central question: why is interest paid? Of course, the many writers who had gone before had not labored in vain. The more worldly of the theologians involved in the usury controversy of the middle ages clearly saw that the rates of interest on loan contracts were linked by arbitrage to the returns that merchants could obtain by directly investing their own capital. An (almost) correct formulation of the instantaneous rate of interest had been offered by W. S. Jevons. And the role of knowledge in the production process had been stressed by J. S. Mill, Alfred Marshall, and J. B. Clark. As Fisher himself emphasized, there was no important idea in his treatment of capital and interest that could not be found somewhere in the public domain when he wrote. But there can be genius in synthesis and Fisher was the man for this difficult job. He began by disposing of a number of unprofitable controversies that had absorbed the energies of earlier writers. (Fisher's fine commentary on the history of interest theory is among the good things left out of the 1930 book.) In particular, the productivity of capital was simply taken for granted. BohmBawerkss effort (still repeated by the authors of some modern textbooks) to ground it in the “superiority of more roundabout methods of production” is incisively rebutted: It is not true that, of all possible productive processes, the longest are the most productive; but it is true that, of all productive processes actually employed, the longest are also the most productive. No one will select a long way unless it is at the same time a better way. All the long but unproductive processes are weeded out.

Again, Fisher gave short shrift to the long debate over how the “factors of production” should be classified. For him the important truths were that anything or anybody that yields an income or service over time is a capital good; that capital goods, both human and non-human, are created by investing income; that the value of a capital good obtained by discounting each of its expected future income by the rate of interest and summing them up; and that, correctly viewed, interest itself is only another name for income. But Fisher's greatest achievement in The Rate of Interest was to bring order into the horribly confused debate between writers who traced the origin of interest toa human preference

for present over future pleasures and those who traced it to the productivity of investment in capital goods. He did so by showing how these two forces interacted at the margin to determine the rate of interest. Some earlier writers—most notably John Rae, J. B. Clark, and B6hm-Bawerk—had moved in the direction of the correct solution but had stumbled when confronted with the difficult mathematical demands of capital and interest theory. Fisher was, along with his many other accomplishments, a professionally trained mathematician of the first rank; in fact, the Yale mathematics department was both saddened and puzzled when, as a young faculty member, he elected to shift to economics in the hope of doing more good in the world. (In common with so many other members of the country’s intellectual elite before World War I, he was the son of a Protestant minister.) Fortunately, Fisher could explain as well as analyze and in this book he gives us the fundamentals of capital and interest not once but three times: with a fixed income, with a variable but known income, and with an income associated with risk. To say that Fisher “could explain” is gross understatement. In his ability to state sophisticated theoretical arguments in clear English, he has had no superiors and few equals. Many economists have aspired to write a book that would appeal to professional colleagues, beginning students, and businessmen. Fisher is one of the handful that ever succeeded. At present writing the reputation of Irving Fisher has

never been higher and, so far as what is taught in the classroom, his influence never greater. It was not always so. In the intellectual confusion that followed the Great Depression, even distinguished economists fell to repeating the absurdity that “interest is mainly a monetary phenomenon” and viewing the interest rate as an uncomplicated control variable to be raised or lowered at the whim of central bankers. It is for students of intellectual history to explain how and why Fisher's truth that expectations about changes in the price level are built into the structure of interest rates virtually faded from view in the years when we were all supposed to have become Keynesians. No doubt Irving Fisher deserves to be remembered and honored in footnotes and memorial lectures. But is it really necessary to read him? (In the so-called hard sciences even the original texts of Einstein and Faraday are left to specialists in the history of science.) The answer, I believe, is yes. The theory of capital and interest may well be the most difficult sub-

discipline in economics. Certainly it is one where preoccupations with money and credit regularly distract attention from fundamentals and one where errors and fallacies have an especially tenacious hold on life. For example, much recent work in capital theory has managed to receive widespread notoriety

by casually ignoring Fisher's truth that labor is not a separate factor of production but simply human capital. Fishers grasp of fundamentals is so firm and his exposition so clear and thorough that, for anyone who wants to learn capital and interest, his great books published in 1906 and 1907 are still the best place to begin. Donald Dewey New York City May, 1982

THE

RATE

OF

INTEREST

THE

MACMILLAN

COMPANY

NEW YORK + BOSTON - CHICAGO ATLANTA + SAN FRANCISCO

MACMILLAN LONDON

THE

& CO., Limrrep

- BOMBAY - CALCUTTA MELBOURNE

MACMILLAN CO. OF CANADA, TORONTO

Lt.

THE ITS

RATE NATURE,

OF

INTEREST

DETERMINATION

AND

RELATION TO ECONOMIC PHENOMENA

BY

IRVING PROFESSOR

OF

FISHER,

POLITICAL

Pu.D.

ECONOMY,

YALE

UNIVERSITY

New Pork

THE

MACMILLAN

COMPANY

1907 All rights reserved

CorpyricHtT,

By THE

MACMILLAN

Set up and printed.

1907,

COMPANY.

Published October, 1907.

Norwood Press J. 8. Cushing Co. — Berwick & Smith Co. Norwood, Mass., U.S.A.

TO

The PMemory OF

JOHN WHO

LAID

THE

UPON I HAVE TO

RAE FOUNDATIONS WHICH

ENDEAVORED BUILD

PREFACE THE problem of interest has engaged the attention of writers for two thousand years, and of economists since And yet, with the exception of what economics began. has been accomplished

by Rae,

Béhm-Bawerk,

Landry,

and some others, very little progress has been made toward Even these writers can scarcely a satisfactory solution. claim to have established a definitive theory of interest. While the value of their work is great, it is chiefly They have cleared the way to a true theory negative. by removing the confusions and fallacies which have beset the subject, and have pointed out that the rate of interest is not a phenomenon restricted to money markets, but is omnipresent in economic relations. The theory of interest here presented is largely based upon the theories of the three writers above mentioned,

and may therefore be called, in deference to Bohm-Bawerk, an “agio theory.” But it differs from former versions of that theory by the introduction explicitly of an income

concept. This concept, which I have developed at length in The Nature of Capital and Income, is found to play a central réle in the theory of interest. The difficult problem is not whether the rate of interest 7s an agio, or premium, for of this there can be no question, but upon what does that agio depend and in what manner? Does it depend, for instance, on the volume of money, the amount of capital, the productivity of capital, the “superior productivity of roundabout

processes,”

the labor of the

capitalist,

the

helplessness of the laborer, or upon some other condition ? vii

Vili

PREFACE

The solution here offered is that the rate of interest depends on the character

of the income-stream, — its size,

composition, probability, and above all, its distribution in time. It might be called a theory of prospective provtsion of income. As in The Nature

of Capital and Income, mathematics have here been relegated toappendices. These appendices are

not,

however,

mere

translations

into mathematical

language of the theory verbally expressed in the text. Mathematics can properly claim no place in economic discussions except as they add something not expressible, or at any rate only imperfectly expressible, in ordinary language. Parts of Chapters V and XIV with their appendices have appeared in somewhat different forms in Appreciation and Interest. My thanks are due to the American Economic Association for permission to use portions of this monograph unaltered. Since it appeared a decade ago, the view expressed in it, to the effect that appreciation of money should, and to some extent does, lower the rate of interest expressed in money, has gained considerable currency, though it is still unfamiliar to most persons. It has been thought wise to present again the

statistical evidence in its favor, and to bring the statistics down to date. In the preparation of this book I have received important aid from many persons. For general criticism I am indebted to my wife, to my colleagues, Professors H. C. Emery and J. P. Norton, and to my friend Richard M. Hurd, President of the Mortgage-Bond Company of New York City. My thanks are also due to Finance Minister Boéhm-Bawerk for his kindness in reading and criticising the chapter devoted to his theory of interest; to Professor Clive Day for facts and references on the history of inter-

est rates; to Dr. Lester W. Zartman for a large part of

PREFACE

ix

the statistical computation and for many helpful criticisms; to two of my students, Mr. Harry G. Brown and Mr. J. H. Parmelee, for valuable aid in proof-reading, including many keen and fruitful suggestions; and to my

brother,

and valuable exposition.

Herbert

criticism

W.

Fisher,

for a most

of the mode

IRVING NEw

HAvEnN, July, 1907.

searching

of expression and FISHER.

CONTENTS FIRST PART

I.

PART

II.

PART

III.

SECOND

PART

IV.

CONCLUSIONS

CRITICISM FIRST

SUMMARY

OF

PREVIOUS

APPROXIMATION

AND

THIRD .

;

.

-

:

APPROXIMATIONS :

OHAPTERS I-IV

THEORIES.

:

:

6

°

V-VII

VIII-XI XTI-X Vit

CONTENTS

xii

SECOND PART

I.

SUMMARY

CRITICISM

OF

PREVIOUS

THEORIES

OHAPTER

I. II.

SY = = § 8. Summary. : : 6 ci : S > : 5 APPENDIX

TO CHAPTER

XI.

TO CHAPTER

XIV.

SratistTicaLt

.

.

:

:

.

:

405 407 408 EM 412

:

:

Z

416

Data

§ 1. Table of interest rates each year in seven countries § 2. References to other statistics of the rate of interest § 3. Index-numbers of prices . INDEX

402

TurirpD APPROXIMATION

§ 1 (to Ch. XI, § 8). Reasons for omitting mathematical statement of third approximation r a : 5 3 . . APPENDIX

3890 3892 3894

:

-

. -

418 421

5

.

429

PART

I.

Criticism

CHAPTER

I.

CuHaptTer

II.

CHAPTER

III.

Cost THEORIES

CHAPTER

IV.

B6OuM-BAWERK’s

CRUDE

THEORIES

PRODUCTIVITY

THEORIES THEORY

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See The Nature of Capital and Income, Chap. IX. 5 Chap. X.

Src. 3]

TIME-PREFERENCE

91

ness. Or, if we prefer to stop just short of this subjective income, we may say that income consists of the objective services which impinge upon our persons and are on the point of producing the subjective effects on consciousness. In short, the income-stream consists of nourishment, clothing, shelter, amusements, the gratification of vanity, and other miscellaneous items. It is this income-stream upon which attention now centers. Henceforth, instead of speaking vaguely and loosely of the preference for present “goods” over future “goods,’’ we shall speak of the preference for present enjoyable income over future enjoyable income. ‘‘Present” and “future” are, of course, used in a comparative sense only; in a more accurate statement we should substitute ‘“‘early”’ and “deferred.” It should be noted that the preference for present over future goods, when thus reduced to its lowest terms, rids the values of the contrasted present and future goods of the interest element. When any other goods than enjoyable income are considered, their values already imply a rate of interest. 7When we say that interest is the premium on the value of present a_ house over-that of a future house,

we are apt to forget that the value of each house is itself based on a rate of interest. |We have seen’ that the price of a house is the discounted value of its future income.) \In the process of discounting there lurks a rate of interest.

The value of houses will rise or fall as the rate of interest falls or rises. Hence, when we compare the values of present and future houses, both terms of the comparison involve the rate of interest. If, therefore, we undertake to make the rate of interest depend on the relative preference for present over future houses, we are making it depend on two elements, in each of which it already enters. The same is true of all capital, and also of those items of income which we have called interactions; for the value of an interaction is the discounted value of the ultimate income 1 See supra, Chap. II, and Chap. XIII.

The Nature

of Capital and

Income,

92

THE

RATE

OF INTEREST

[Cuap. VI

to which that interaction leads. We could not rest satisfied in the statement that interest is the premium on the value of present tree-planting over that of future treeplanting; for the value of each tree-planting itself depends on the rate at which the future income from the tree is discounted. But when present ultimate income is compared with future ultimate income, the case is different, for the value of ultimate income involves no interest whatever. We see, therefore, that the reduction of the problem of interest to a comparative value of present and future enjoyable income avoids the difficulty of making interest depend on magnitudes which themselves depend directly on interest. §4

Having seen that time-preference is really a preference for early enjoyable income compared with remote enjoyable income, we next note that this preference depends on the entire future income-stream, that is, the amount of income and the manner in which it is distributed in time. It depends on the relative abundance of the early and remote incomes — or what we may call the time-shape of the income-stream. If future income is particularly abundant, its possessor would evidently be willing to sacrifice a large amount of it for the sake of a relatively small amount of present income.’ Thus, in winter, the possessor of a strawberry patch might be willing to sell two boxes of strawberries, due in six months, for one available to-day, while in strawberry season he might, on the contrary, be + It is noteworthy that, though lacking any definite theory of income, those writers who have made the most successful analysis of the rate of interest have, in substance, made it depend, to some extent, at least, on income. Thus Béhm-Bawerk, as has been observed,

gives as one of the “three circumstances” affecting the “preference for present goods” the ‘‘relative provision for present and future”’; and Landry virtually states the same relation, on p. 55 of L’Intérét du Capital.

Sxc. 4]

TIME-PREFERENCE

93

willing to give up two boxes of his then abundant crop for the right to one box in the succeeding winter. It is, therefore, not necessary here to distinguish, as Bohm-Bawerk does, between the principles which lead to the existence of interest and those which regulate the rate of interest; for to determine the rate of interest will include the determination of whether the rate must necessarily always be greater than zero. As a matter of fact, the rate may theoretically be negative, as in the case just mentioned of strawberries in strawberry season, or in the case cited by Bohm-Bawerk himself, of ice in winter. The reason such negative interest is not actually encountered in the market is that perishable articles such as ice and strawberries are never used as standards of value. We express our rates of interest in money, even if our contracts relate to strawberries or ice. But money possesses durability, and may be hoarded without loss. This explains why the rate of interest in terms of money can never be negative.} The proposition that the preference of any individual for present over future income depends upon his prospective enjoyable income corresponds to the proposition in the theory of prices, that the marginal utility of any article depends upon the quantity of that article; both propositions are fundamental in their respective spheres. When it is said that the time-preference of an individual depends on his enjoyable income, it is meant that the rate of preference for, say, $100 worth of this year’s enjoyable income over $100 worth of next year’s enjoyable income depends upon the entire character of the individual’s income-stream.

An income-stream is made up of a large number of different elements, some of which contribute to nourishment, others to shelter, others to amusement, etc. In a

complete enumeration of these elements, we should need to distinguish the use of each different kind of food, the 1See Supra, Chap. V, § 5.

94

THE RATE

OF INTEREST

(Cuar. VI

gratification of every variety of human want. Each of these constitutes a particular filament of the incomestream, extending from the present out into the indefinite future and varying at different points of time in respect to size and probability of attainment. A man’s rate of time-preference, therefore, depends on the size and probability at various moments of the entire collection of income-elements. For the graphic representation, however, of size and distribution in time, it is simpler to lump together these innumerable elements of income, expressed in terms of money. We may say, therefore, that an individual’s time-preference depends on the following four elements : — 1. On the size of the income-stream. 2. On its distribution in time,—according as it accrues evenly or unevenly, and if unevenly, according to the periods at which it is‘expected to be relatively abundant and the periods at which relatively scarce. 3. On the composition of the income-stream,—what part consists of nourishment, what part clothing, what part shelter, etc. 4, On the probability of the income-stream and its constituent elements. We shall consider these in order.

§5 Our first step, then, is to show how a person’s timepreference depends on the size of his income. In general, it may be said that the smaller the income the higher is the preference for present over future income. It is true that a small income implies a keen appreciation of future wants as well as of immediate wants. Poverty bears down heavily on all parts of a man’s life, both that which is im-

Sxc. 6]

TIME-PREFERENCE

95

mediate and that which is remote. But it enhances the utility of immediate income even more than of future income. This result is partly rational, because of the importance, by supplying present needs, of keeping up the continuity of life and the ability to cope with the future; and partly irrational, because the pressure of present needs blinds one to the needs of the future. As to the rational side, it is clear that present income is absolutely indispensable, not only for the present, but even as a precondition to the attainment of future income. ‘A man must live.” Any one who values his life would prefer to rob the future for the benefit of the present, so far, at least, as to keep life

going.

If one has only one loaf of bread he would not

preserve it for next year; for if he did he would starve in the meantime. A single break in the thread of life suffices to cut off all the future. And not only is a certain minimum of present income necessary to prevent starvation, but the nearer this minimum is approached the more precious does present income appear, relatively to future income. As to the irrational side, the effect of poverty is often to relax foresight and self-control and tempt one to “trust to luck” for the future, if only the all-absorbing clamor of present necessities is satisfied. We see, then, that a low income tends to produce a high time-preference, partly from lack of foresight and self-control, and partly from the thought that provision for the

present is necessary both for itself and for the future as well.

§ 6

We come next to the influence upon time-preference of

the distribution of income in time — the time-shape of the income-stream. The concept of the time-shape of one’s income-stream is fundamental in the following chapters.

Four different types of time-shape may be distinguished:

THE

96

[Cuap. VI

OF INTEREST

RATE

uniform income, as represented in Figure

2;* increasing

income (Fig. 3) ; decreasing income (Fig. 4) ; and fluctuating —

nr

nna

re

Fia. 2.

income (Fig. 5). The effect of possessing an increasing income is to make the preference for present over future

:

=.

Fie. 3.

income higher than otherwise, for it means that present income is relatively scarce and future income abundant.

RE

RAR

A

A

ER

Fia. 4.

A man who is now enjoying an income year, but expects in ten years to be $10,000 a year, will prize a dollar to-day dollar due ten years hence. He may,

of only $1000 a enjoying one of far more than a in fact, borrow

1 In these curves, time is represented horizontally and rate of flow of income vertically, as in The Nature of Capital and Income, Chap. XIII.

Sec. 6]

TIME-PREFERENCE

97

money to eke out this year’s income, and make repayment by sacrificing from the more abundant income ten years later. Reversely, a gradually decreasing income, making, as it does, present income relatively abundant and future income scarce, tends to reduce the preference for present as compared with future income. A man who has a salary of $10,000 at present, but expects to retire in a few years on half pay, will not have a very high preference for present income over future. He will want to save from his present abundance to provide for coming needs. The extent of these effects will of course vary greatly with different individuals. Corresponding to a given ascend-

Fig. 5.

ing income, one individual may have a preference of 10 per cent., and another only 4 per cent. What we need here to emphasize is merely that, given a descending instead of an ascending income, both of these individuals would

experience areduction of time-preference,

— the first, say,

to 5 per cent. and the second, say, to 2 per cent. If we consider the combined effect on time-preference of both the size and time-shape of income, we shall observe that those with small incomes are much more sensitive to time-shape in their feeling of time-preference than are those with large incomes. For a poor man, a very slight

stinting of the present suffices to enhance enormously his preference for present over future income; and reversely, a very slight increase in his present income will suffice to H

98

THE

RATE

OF INTEREST

([Cuap. VI

enormously lessen that preference. A rich man, on the other hand, requires a relatively large variation in the comparative amounts of this year’s and next year’s income to suffer any material change of time-preference. It is clear that the dependence of time-preference on time-shape of income is practically identical with what Béhm-Bawerk calls the “first circumstance” making for the superiority of present over future goods:* “The first great cause of difference in value between present and future goods consists in the different circumstances of want and provision in present and future. . . . If a person is badly in want of certain goods, or of goods in general, while he has reason to hope that, at a future period, he will be better off, he will always value a given quantity of immediately available goods at a higher figure than the same quantity of future goods.”

§ 7 We come next to the influence of the composition of the income-stream on the time-preference of its possessor. An income worth $5000 may, for one individual, comprise one set of enjoyable services, and for another, an entirely different set. The inhabitants of one country may have relatively more house-shelter and less food-element in their incomes than those of another. These differences will have an influence in one direction or the other upon the time-preference. Diminution of any one constituent of income would have an effect upon the time-preference

similar to the effect of diminution of income in general.

A

decrease of the food element would be felt especially, both because this element usually forms a considerable part of

income and because it is a prime necessity. Were we to pursue the subject in detail, we should need to resolve a person’s income into the elements of which it is composed, — nourishment, shelter, clothing, and other gratifications. As we have seen, the income-stream is a complex magnitude consisting of a large number of sepa1 The Positive Theory of Capital, p. 249.

Szc. 8]

TIME-PREFERENCE

99

rate filaments, one for each separate constituent. Any individual’s rate of preference depends on this complex magnitude in its entirety. Theoretically a change in any of these individual partial income-streams will influence the rate of preference. A bread famine, a large wheat crop, the outlook for the fuel supply, electric light service, shoes, or diamonds, all should be taken into account in a statement designed fully to cover the influence of the income-stream upon time-preference. It is not necessary to formulate the concept of ‘“‘composition” of an income-stream in such a way as to divorce it from the concepts of size and time-shape; for the composition of an income-stream is included in a statement

of the size and time-shape of each filament of which that income-stream consists. We content ourselves by considering all these elements of income lumped together in a single sum of money value. We need not here concern ourselves with the principles which govern the valuation of the sum. These principles constitute the theory of prices, not of interest; and these prices, as we have already observed, being prices of final or enjoyable elements of income, do not, like the prices of capital or of interactions, embarrass us by direct dependence on the rate of interest which we are seeking to solve. Assuming, then, the elements of which incomes are composed, to be adjusted according to the principles which regulate

prices, we shall hereafter usually treat an income-stream as a homogeneous quantum expressible in terms of gold or some other monetary standard. Our task is therefore reduced to answering the question: Enjoyable incomes being expressed in terms of money, what determines the rate of

interest in terms of this same money?

§8

We come finally to the element of risk. Income, being future, is always subject to some uncertainty, and this un-

100

THE

RATE

OF INTEREST

(Cuap. VI

certainty must naturally have an influence on the rate of time-preference of the possessor. We have seen that timepreference is the preference for $1 certain added to immediate income over $1, also certain, added to income one year hence. The influence of risk on time-preference therefore means the influence of uncertainties in the anticipated income of an individual upon his relative valuation of present and future small increments of income, both increments being certain. The manner in which risk operates upon time-preference will differ according to the particular periods in the future to which the risk applies. If the possessor of income regards the income of the immediate future as fairly well assured, but fears the loss of income in more remote periods, he may be aroused to a high appreciation of the needs of that remote future and save from his present certain abundance in order to provide for the later possible scarcity. Income in which this sort of risk exists:tends, therefore, to produce a low rate of time-preference for income which is immediate and certain as compared with income which is remote and uncerThe tain. In actual fact, such a type is not uncommon. remote future is usually less known than the immediate future. This means that the risk connected with distant income is greater than that connected with income near at hand. The chance of disease, accident, disability, or death is always to be reckoned with, but under ordinary circumstances is greater in the remote future than in the immediate future. Consequently there is usually a tendency toward a low time-preference. This tendency is expressed in the phrase to “lay up for a rainy day.”’ But the influence of risk is not always in the direction of lowering time-preference. Sometimes the relative uncertainty is reversed, and immediate income is subject to higher risk than remote income. Such is the case in war or other temporary threat of misfortune. Such is also the case when an individual is assured a permanent

position with a salary after a certain time, but in the mean-

Sxc. 8]

TIME-PREFERENCE

101

time must obtain a precarious subsistence. In these cases the effect of the risk element is to enhance the estimation in which immediate income is held. Again the risk may, instead of applying especially to remote periods or especially to immediate periods, apply to all alike. Such a condition largely explains why salaries and wages are lower than the average earnings of those who work for themselves. Those who choose salaries rather than profits are willing to accept a low income in order to get rid of a precarious one. Since arisky income, if the risk applies evenly to all parts of the income-stream, is nearly equivalent to a low income, and since a low income, as we have seen, tends to create a high time-preference, risk, if uniformly distributed in time, must tend to raise time-preference. We see, then, that risk tends in some cases to increase and in others to decrease the rate of time-preference. But there is a common principle in all these cases. Whether the result is a high or a low time-preference, the primary

fact is that the risk of losing the income in a particular period of time operates as a virtual impoverishment of the income in that period, and hence increases the estimation in which it is held. If that period is a remote one, the risk to which it is subject makes for a high appreciation of remote income; if the period is the immediate future, the risk makes for a high appreciation of immediate income; if the risk is in all periods of time, it acts as a virtual decrease of income all along the line. There are, however, anomalous individuals in whom caution is absent or perverted. Upon these, risk will have quite the opposite effects. Some persons, who see great speculative chances in the remote future, may treat that future as though it were especially well-endowed, and there-

fore be willing to sacrifice a large amount of their “great expectations” in the future for the sake of a relatively small addition to their present income. In other words, they will have a high time-preference. The same individuals, if receiving an income which is risky for all periods

102

THE

RATE

OF INTEREST

[Cuap. VI

of time alike, might have, as a result, a low instead of a high time-preference. The income to which risk applies may be either the income from articles of capital external to man, or the income from man himself. In the latter case the risk of losing the income is the risk of death or invalidism. This risk — the uncertainty as to human life and health — differs somewhat from the uncertainty of income dependent on objective capital; for the cessation of life not only produces a cessation of income from the human machine, but a cessation of the enjoyment of all income whatsoever. For persons who have children whose future welfare they have at heart, this consideration loses much of its force. A man with wife and children is willing to pay a high insurance premium in order that they may continue to enjoy an income after his death, while an unmarried man, or a@ man who cares only for self-indulgence and wishes to “make the day and the journey alike,” will not try to con-

tinue the income after his death. Uncertainty of life in the latter case is especially calculated to produce a high degree ef time-preference. Sailors offer a good example. They are natural spendthrifts, and when they have money use it lavishly. The risk of shipwreck is constantly before them, and their motto is, “A short life and a merry one.’ The effect of risk, therefore, is manifold, according to the degree and range of application of risk to various periods of time; according to the cautious or incautious character

of the individual; according to whether or not the risk in question applies to human life, and if so, according to whether or not the individual’s interest in the future extends beyond his own lifetime. The manner in which these tendencies operate upon the rate of interest will be discussed in Chapter XT. §9 The proposition that the preference for present over future income depends upon the income, its size, time-

Src. 9]

TIME-PREFERENCE

103

shape, composition, and probability, does not deny that it may depend on other factors also, just as, in the theory

of prices, the proposition that the marginal utility of an

article depends upon the quantity of that article does not deny that it may depend on other elements as well. But the dependence of time-preference on income is of most

importance, for time-preference is a preference for income. It is in the same way that the dependence of the marginal utility of bread on the quantity of bread is more important than its dependence on the quantity of some other commodity, such as butter. As to the dependence of this timepreference for income on other factors than that income, these other factors may conveniently be regarded as affecting the “ form of the function” which expresses its dependIn this light may be considered the ence on income. influence of “the personal equation.” It is clear that the rate of time-preference which corresponds to a specific income-stream will not be the same for everybody. One man may have a time-preference of 5 per cent. and another 10 per cent., although both have the same income. The difference will be due to the personal characteristics of the individuals. These characteristics are chiefly five in number:' (1) foresight, (2) self-control, (3) habit, (4) expectation of life, (5) interest in the lives of other persons. We shall take these up in order. (1) First, as to foresight. Generally speaking, the greater the foresight, the less the rate of time-preference, and vice versa.” In the case of primitive races and uninstructed 1Cf. Rae’s Sociological Theory of Capital, p. 54. Also BéhmBawerk, The Positive Theory of Capital, Book V, Chap. III. 2 To be exact, we should observe that lack of foresight may either increasé or decrease time-preference. Although most persons who lack foresight err by failing to give due weight to the importance of future needs, or, what amounts to the same thing, by overestimating the provision existing for such future needs, cases are not lacking in which the opposite erroriscommitted; that is, the individual exaggerto be ates the needs of the future or underestimates the provision likely In order not to complicate the text, only the former made for them.

104

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[Cuap. VI

classes of society, the future is seldom considered in its true proportions. The story is told of such a person that he would not mend his leaky roof when it was raining, for fear of getting more wet, nor when it was not raining, because he did not then need shelter. Among such persons, the preference for present gratification is powerful because their comprehension of the future is weak. In regard to foresight, Rae states: *— “The actual presence of the immediate object of desire in the mind, by exciting the attention, seems to rouse all the faculties, as it were, to fix their view on it, and leads them to a very lively conception of the enjoyments which it offers to their instant possession. The prospects of future good, which future years may hold out to us, seem at such a moment dull and dubious, and are apt to be slighted, for objects on which the daylight is falling strongly, and showing us in all their freshness just within our grasp. There is no man, perhaps, to whom a good to be enjoyed to-day, would not seem of very different importance, from one exactly similar to be enjoyed twelve years hence, even though the arrival of both were equally certain.”

The sagacious business man represents the other extreme; he is constantly forecasting. These differences in degrees of foresight produce corresponding differences in

the dependence of time-preference on the character of income. Thus, for a given income, say $1000 a year, the reckless might have a time-preference of 10 per cent., when the forehanded would experience a preference of only 5 per cent. In both cases the preference will depend on the size of the income, being higher the lower the income; but the particular rates corresponding to a particular income in the two cases will be entirely different. Therefore the rate of preference, in general, will be higher in a com-

munity

consisting of reckless

individuals

than in one

consisting of the opposite type. and more common error will be hereafter referred to when “lack of foresight”’ is mentioned. But the reader may in each such case readily add the possibility of the contrary error.

? Sociological Theory of Capital, p. 54.

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105

(2) We come next to self-control. This trait, though distinct from foresight, is usually associated with it and has very similar effects. Foresight has to do with thinkwg, self-control with willing. A weak will usually goes with a weak intellect, though not necessarily, and not always. The effect of a weak will is similar to the effect of inferior foresight. Like those workingmen who cannot carry their pay home Saturday night, but spend it on the way in the grogshop, many persons cannot deny themselves any present indulgence, even when they know definitely what the consequences will be in the future. Others, on

the contrary, have no difficulty in stinting themselves in the face of all temptations. (8) The third characteristic of human nature which needs

to be considered is habit. That to which one is accustomed exerts necessarily a powerful influence upon his valuations and therefore upon his time-preference. ‘This influence may be in either direction.

Rich men’s sons, accustomed

to the enjoyment of a large income, are apt to valuation on present compared with future would persons of the same income who were under different conditions. If they suffer

put a higher income than brought up a reverse of

fortune, they find it harder to live moderately than those of equal means who have risen instead of fallen in the

economic scale; and this will be true even if foresight and self-control are the same in the two cases. (4) The fourth circumstance which may influence the form of the function by which time-preference depends on the character of income has to do with the uncertainty of life of the recipient of that income. We have already seen in a different connection that the time-preference of an

individual will be affected by the prospect of a long or short life, both because the termination of life brings the termination of the income from labor, and because it also terminates the enjoyment of all income. It is the latter fact in which we are here interested; the expectation of life affects the dependence of time-preference on income. There

106

THE RATE

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[Cuar. VI

will be differences among different classes, different individuals, and different ages of the same individual. So far as age is concerned, the usual course of events is as follows: The time-preference in the early periods of life is high because foresight and self-control are weak. Children are notorious spendthrifts. A little later, when the individual has acquired some self-control and foresight, he will still have a high rate of preference, but for another reason, —the prospect of an ascending inHis present income is small, but he looks come-stream. forward to having an ample income in five or ten years. As the time of marriage and middle life approaches, the opposite tendency may assert itself. Foreseeing the needs of middle life and anticipating no increase in the provision for those needs, he will cease to borrow and begin to save. After he has passed middle age, when his children have become self-supporting, and he looks forward to declining years, matters are reversed again. He will want to enjoy his income while he may, the income beyond his death being of no significance to him except as it The prospect can be bequeathed to his descendants. of death plays an important rdéle in the thoughts of the old. One evidence of this is the prominence given to it in all philosophical and religious systems.' The philosophy of Horace, for instance, was summed up in the maxim “carpe diem,” which is practically the same as the still older maxim, “eat, drink, and be merry, for tomorrow we die.” The chance of death may be said to be the most important rational factor tending to make the rate of time-preference high, and anything that would

tend to prolong human life would tend at the same time to reduce the rate of time-preference. As Rae says:? — “Were life to endure forever, were the capacity to enjoy in perfection all its goods, both mental and corporeal, to be prolonged ‘See Metchnikoff, Nature of Man, English translation, New York

(Putnams), 1903, Part II.

® The Sociological Theory of Capital, pp. 53-54.

Sxc. 9]

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107

with it, and were we guided solely by the dictates of reason, there could be no limit to the formation of means for future gratification, till our utmost wishes were supplied. A pleasure to be enjoyed, or a pain to be endured, fifty or a hundred years hence, would be considered deserving the same attention as if it were to befall us fifty or a hundred minutes hence, and the sacrifice of a smaller present good, for a greater future good, would be readily made, to whatever period that futurity might extend. But life, and the power to enjoy it, are the most uncertain of all things, and we are not guided altogether by reason. We know not the period when death may come upon us, but we know that it may come in a few Why then be providing days, and must come in a few years. goods that cannot be enjoyed until times, which, though not very remote, may never come to us, or until times still more remote, and which we are convinced we shall never see? If life, too, is of uncertain duration and the time that death comes between us and all our possessions unknown, the approaches of old age are at least certain, and are dulling, day by day, the relish of every pleasure.”

The shortness of life thus tends powerfully to raise the rate of time-preference. This is especially evident when the income-streams compared are long. A lover of music will prefer a piano at once to a piano available next year, because, since either will outlast his own life, he will get one more year’s use out of the piano available at once. From what has been said it is clear that there are three

periods in his life when a man’s time-preference is especially high: (1) in early life it is high because of youthful recklessness; (2) in the preparatory stage, because future income seems relatively abundant; and (3) late in life, because future income seems relatively superfluous. (5) But whereas the shortness or uncertainty of life tends

to raise the rate of time-preference, its effect is greatly mitigated by the fifth circumstance, the care for the welfare of posterity. Probably the most powerful cause tending to reduce the rate of interest is the love of one’s children and the desire to provide for their good. When these sentiments decay, as they did at the time of the decline and fall of the Roman Empire, and the fashion is to exhaust wealth in

108

THE RATE

OF INTEREST

[Cuarv. VI

self-indulgence and leave little or nothing to offspring, the rate of time-preference and rate of interest will be high. At such times the motto, “After us the deluge,” indicates the feverish desire to squander in the present, at whatever cost to the future.’ In a community like the United States, where parents regard their lives as continuing after death in the lives of their children, there exists a high appreciation of the needs of the future which tends, therefore, to produce a low rate of time-preference. It is this sentiment which is responsible for the enormous extension of life insurance. At present in the United States the insurance on lives amounts to $20,000,000,000. This represents, for the most part, an investment of the present generation for the next. The investment of this sum springs out of a low time-preference, and tends to produce a low rate of interest. Not only does the regard for posterity lower interest, but the increase of posterity has in part the same effect. So far as an increase in the size of a family reduces the income per capita of that family, it operates, like impoverishment, to increase time-preference. So far as it adds to future needs rather than to immediate needs, it operates, like a descending income-stream, to diminish time-preference. Parents with large families feel the importance of providing for future years far more than parents otherwise similar but with small families. They try harder to save and to take out life insurance. In other words, their rate of preference for present over future income is lowered. An increase of population, therefore, will, other things being equal, reduce the rate of interest. This proposition must not be thought to conflict with the reciprocal proposition that the same prudent regard for the future which is created by the responsibilities of parenthood itself tends to diminish the number of offspring. An increase of population tends toward a low time-preference, but reciprocally a low * See Rae, The Sociological Theory of Capital, Daoiie

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TIME-PREFERENCE

109

time-preference tends to check such increase. that the thrifty Frenchman and Scotchman families.

Hence it is have small

§ 10

Time-preference, therefore, depends for each individual on his income; that is, its size, time-shape, composition, and probability; but the form of this dependence differs according to the various circumstances of the individual. The circumstances which will tend to make his timepreference high are (1) shortsightedness, (2) a weak will,

(3) the habit of spending freely, (4) the shortness and uncertainty of his life, (5) selfishness, or the absence of any The reverse conditions desire to provide for posterity.

will tend to make his rate of preference low; namely, (1) a high degree of foresight, which enables him to give to the future

such attention as it deserves;

(2) a high

degree of self-control, which enables him to abstain from present income in order to increase future income; (3) the habit of thrift; (4) the probability of long life; (5) the possession of a family and a high regard for their welfare after his death. The resultant of these various tendencies in any one in-

dividual will determine the degree of his time-preference in relation to any particular income. This result will differ as between individuals, and as between different times for the same individual. The essential fact, however, is that

for any given individual at any given time, his time-prejerence depends in a definite manner

upon

the size, shape,

composition, and probability of his income-stream.

§ 11 This view, that the rate of time-preference and consequently the rate of interest depend upon income, needs to be contrasted with the common view, which makes the

110

THE RATE OF INTEREST

(Cuap. VI

rate of interest depend merely on the scarcity or abundance of capital. It is commonly believed that where capital is scarce, interest is high, and where capital is plentiful, interest is low. In a general way there is undoubtedly some truth in this proposition; and yet it contains a misinterpretation of borrowing and lending. It is true that when and where men are anxious to lend, interest is low, and when and where men are anxious to borrow, interest is high. But it is not true that the more capital a man has the more anxious he is to lend, and the less capital he has the more anxious he is to borrow. The willingness to lend or borrow depends primarily, not upon the amount of one’s capital, but upon the character of the income which he gets from it, — whether this income is large or small, immediate or deferred, of what elements it consists, whether it is certain or uncertain. The proposition that abundance of capital tends to lower interest is thus very superficial; for abundant capital merely means abundant income. Capital-value is discounted income. Behind, or rather beyond, a capital of $100,000 is the income which that capital represents. To fix attention on the $100,000 capital instead of on the income is to use the capital as a cloak to cover up the real factor in the case. Moreover, capital-value is itself dependent on the rate of interest. The capital-value of a farm will be doubled if the rate of interest is halved. In such a case there would be found more capital in farms; for the farms in a community would rise; say, from $10,000,000 to $20,000,000. But it is not the rise in capital which produces the fall in interest. On the contrary, it is the fall in the interest rate which produces the rise in the valuation of capital. If we attempt to make the rate of interest depend on capital-value, then, since capital-value depends on two factors, — the prospective income and the rate of interest, —we thereby make the interest rate depend partly on income and partly on itself. The dependence

on itself is of course nugatory, and we are brought back to

Ssc. 11)

TIME-PREFERENCE

111

its dependence on income as the only fact of real significance. But even as thus amended and explained, the proposition that the rate of interest depends on the amount of capital is not satisfactory. The mere amount of capital does not tell us much about the income for which that capital stands. To know that one man has a capital worth $100,000, and another $200,000, shows, to be sure, that the latter man

may have an income of double the value of the former; but it tells us absolutely nothing as to the “time-shapes”’ of the two incomes; and the time-shape of income has, as we have seen, a most profound influence on the time-

preference of its possessor. Let us suppose two communities similar in population,

distribution of wealth, and all other particulars except in the amount of their capital and the character of the income which that capital represents. One of these two communities we shall suppose has a capital of $100,000 invested, as in Nevada, in mines and quarries nearly exhausted, while in the other community there is $200,000 of capital invested in young orchards and forests, as in Florida. According to the theory that abundance of capital makes interest low,

we should expect the Nevada community to have a high rate of interest compared with the Florida community. But it is evident that, unless other circumstances should interfere, the opposite would be the case; for Nevada has to contemplate a decreasing future income, and in order to offset the depreciation of capital which follows from this condition,’ she would be seeking to lend or invest part of

the income of the present or immediate future, in the hope of offsetting the decreased product of the mines in the more remote future.

The Florida planters, on the contrary, would

be inclined to borrow against their future crops. If the two communities are supposed to be commercially connected, it would be Nevada which would lend to Florida, notwithstanding

the fact that the lending community

was

1 See The Nature of Capital and Income, Chap. XIV.

the

112

THE RATE

OF INTEREST

[CHap. VI

poorer in capital of the two. From the illustration it is clear that the mere amount of capital-value is not only a misleading but a very inadequate criterion of the rate of interest. Apologists for the common statement that abundance or scarcity of capital lowers or raises interest might be inclined to argue that it is not the total capital, but only the “loanable capital” which should be included, and that the Nevada community had more “‘loanable capital’ than the Florida community. But the phrase “‘loanable capital” is merely another cloak to cover the fact that it is not the amount of capital, but the decision to lend or borrow it, which is important. To give this proposition meaning, “loanable capital’? must be taken, not in the literal sense of capital which can be lent, —for all capital is loanable in this sense; but in the sense of capital which persons are willing to lend. Hence, to state that in any community there is abundance of loanable capital is merely to state that there is in that community a willingness to lend a great deal of capital. Consequently, the proposition that the rate of interest, or preference for present over future goods, is low when loanable capital is abundant becomes reduced to the platitude that the rate of preference for present over future goods is low when men wish to lend. But it may be said, surely in a money market there exists at one time a large visible supply of loanable money and at another time a small visible supply, and this supply affects the rate of interest. This, again, is a true but a superficial statement. A little examination will show that the abundance or shortage of loanable bank funds is merely a measure of the decision of merchants to discount or deposit, — in other words, to borrow or lend, —and does not give us any clew as to the reason why they do so. The money or credit

: One of the few defects in Rae’s analysis of interest is his emphasis on the accumulation of capital. Since this accumulation is sae in anticipation of future income, the emphasis belongs on the atter.

Src. 12]

TIME-PREFERENCE

113

is, of course, the mere vehicle by which the bank acts as an intermediary or broker between borrowers and lenders, and does not represent any independent factor in the case. We end, therefore, by emphasizing anew the importance of fixing our eyes on income and not on capital. It is only as we look through capital-value, beyond to the income which it represents, that we reach the efficient causes which operate upon the rate of interest. The absence hitherto of a definite theory and conception of income has prevented economists from doing this. Borrowing and lending are in form a transfer of capital, but they are in fact a transfer of income of which that capital is merely the present value. In our theory of interest, therefore, we have to consider not primarily the amount of capital of a community, but the income for which that capital stands.

§ 12 Unfortunately for purposes of exposition, the relation between time-preference and income cannot be expressed in a simple schedule or curve, as can the relation between demand and price, or supply and price, or utility and quantity consumed, for the reason that income means not a

single magnitude merely, but a conglomeration of a number of magnitudes. As mathematicians would express it, to state that time-preference depends on the character of income, its size, shape, composition, and probability, is to state that time-preference is a function of all the

different magnitudes which need to be specified in a complete description of that income. A geometrical representation, therefore, of the dependence of time-preference on the various magnitudes which characterize income, would be impossible. For a curve can only represent the depend-

ence of a magnitude on one independent variable; even

a surface can only represent dependence on two; but for our requirements we should need a space of n dimensions.

We may represent the relation between I

time-preference

114

THE

RATE

OF INTEREST

[Cuar. VI

and income by a “schedule” like the ordinary “demand schedule” and “supply schedule,” if we make a list of all possible incomes, specifying for each individual income all its characteristics, — its size, time-shape (that is, its relative magnitude for each successive time-interval considered), its composition (or the amount, at each period, of each individual constituent, as nourishment, shelter, etc.), and the certainty or uncertainty attached to all these elements. Having thus compiled a list of all possible incomes, it would only be necessary for us to assign to each of them the rate of

time-preference pertaining to it. Such a schedule would be too complicated and cumbersome to carry out in detail; but the following will roughly indicate some of the main groups of which it would consist. In this schedule we have represented by the three vertical lines three different classes of income, — two extreme types and one mean type, — so that the corresponding rates of time-preference range themselves in a descending series of numbers. We have also represented by the three vertical columns three different classes of individuals, two being of extreme types of individuals, and the third of a mixed or medium type. Thus the numbers in the table descend as we proceed either down or toward the right, the lowest number of all being in the lower right-hand corner,

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Out of the large number of possible incomes represented in such a schedule, of course only one can be the actual income of the individual. The one which exists in any case is to a large extent a matter of choice, as we shall see in the next chapter. Since time-preference may be varied by voluntarily varying the character of the income-stream on which it depends, it follows that the shortsighted, weakwilled spendthrift individual may not have, as a matter of fact, any higher rate of time-preference than his farsighted, self-controlled, abstemious brother. In fact, where a loan market is in full operation, the tendency is for the two in-

dividuals to select such incomé-streams as will bring their time-preference into unison. How this is accomplished will form the subject of the following chapter.

CHAPTER

VII

FIRST APPROXIMATION TO THE THEORY OF INTEREST (ASSUMING INCOME RIGID) § 1

In the last chapter we saw that the rate of preference for present over future goods was, in the last analysis, a preference for present over future income; that this preference depends, for any given individual, upon the character of his income-stream, —its size, time-shape, composition, and probability, — and that the nature of this dependence varies with different individuals. The question at once arises, will not the rates of preference of different individuals be very different, and if so, what relation do these different rates have to the rate of interest? John Rae assumed that the rates differed widely, and that the rate of interest was a sort of average of their different magnitudes. But this is incorrect. In a nation of hermits, in which there was no mutual lending and borrowing, the time-preferences of individuals would diverge widely; but in modern society, borrowing and lending tend to bring into equality the rates

of preference in different minds. It is only because of the limitations of the loan market that absolute equality is not reached. The chief limitation to lending is due to the risk involved, and to the difficulty or impossibility of obtaining the security necessary to eliminate or reduce that risk. Those who are most willing to borrow are oftentimes those who

are least able to give security. It will then happen that these persons, shut off from the loan market, experience a higher rate of time-preference than the rate of interest ruling 117

118

THE

RATE

OF

INTEREST

(Cuar. VII

in that market. If they can contract loans at all, it will be only through the pawn shop or other high-rate agencies. But, for the moment, let us assume a perfect market, in which the element of risk, is entirely lacking, both with respect to the certainty of the expected income-streams belonging to the different individuals, and with respect to the certainty of repayment for loans. In other words, we assume that each individual is initially possessed of a foreknown income-stream, and that he is free to exchange

any part of it to some other person, in consideration of receiving back at some future time an addition to his income for the prospective period. We assume further that to buy and sell various parts of his income-stream (by

loans, etc.), is his only method of altering that incomestream. Prior to such exchange, his income-stream is rigid, t.e. fixed in size, time-shape, and composition.

The

capital-instruments which he possesses are each capable of only a single definite series of services contributing to his income-stream. These assumptions that each man’s income-stream is initially certain and fixed, will be used in our first approximation to the theory of interest. § 2

Under these hypothetical conditions, the rates of timepreference for different individuals would be perfectly equalized. Borrowing and lending evidently affect the time-shape of the incomes of borrower and lender; and since the time-shape of their incomes affects their timepreference, such a modification of time-shape will react upon and modify their time-preference, and bring the market into equilibrium.

If, for any particular individual, the rate of preference differs from the market rate, he will, if he can, adjust the time-shape of his income-stream so as to harmonize his preference rate with the interest rate. Those who, for a given

income-stream, have a rate of preference above the market

Sc. 2]

FIRST

APPROXIMATION

119

rate, will sell some of their surplus future income to obtain an addition to their present meagerincome. This will have the effect of enhancing the value of the future income and

decreasing that of the present. The process will continue until the rate of preference of this individual is equal to the rate of interest. In other words, a person whose

preference rate exceeds the current rate of interest will

to the point which will make the two rates equal. those who, with a given income-stream, have a rate below the market rate, will sell some of their present income to eke out the future, the effect being to increase their preference rate until it also harmonizes with the rate of interest. borrow up Reversely, preference abundant

To put the matter in figures, let us suppose the rate of interest is 5 per cent., whereas the rate of preference of a

particular individual is 10 per cent. Then, by hypothesis, the individual is willing to sacrifice $1.10 of next year’s income in exchange for $1 of this year’s. But in the market he is able to obtain $1 for this year by spending only $1.05 of next year. This ratio is, to him, a cheap price. He therefore borrows, say, $100 for a year, agreeing to return $105; that is, he contracts a loan at 5 per cent. when he is willing to pay 10 per cent. This operation,

by increasing his present income and decreasing his future, tends to reduce his time-preference from 10 per cent. to, say, 8 per cent. Under these circumstances he will borrow another $100, being willing to pay 8 per cent., but having to pay only 5 per cent. This operation will still further

reduce his time-preference, until it has been finally brought down to 5 per cent. Then, for the last or “marginal” $100, his rate of time-preference will agree with the market rate of interest. As in the general theory of prices, this marginal rate, 5 per cent., being once established, applies indifferently to all his valuations of present and future income. Every comparative estimate of present and future which he actually makes must be “on the margin” of his income-stream as actually determined. The above-men-

120

THE

RATE

OF

INTEREST

(Cuapr. VII

tioned 10 per cent. and 8 per cent.rates are not actually experienced by him ; they merely mean the rates of prefererence which he would have experienced had his income not been transformed to the time-shape correspondent to 5 per cent.

In like manner, if another individual, entering the loan market from the other side, has a rate of preference of 2 per cent., he will become a lender instead of a borrower. He will be willing to accept $102 of next year’s income for $100 of this. But in the market he is able, instead of the $102, to get $105. As he can lend at 5 per cent. when he would gladly do so at 2 per cent., he jumps at the chance and invests, not one $100 only, but another and another. But his present income, being reduced by the process, is now more highly esteemed than before, and his future income, being increased, is less highly esteemed. The result will be a higher relative valuation of the present, which, under the influence of successive additions to the sums lent, will rise gradually to the level of the market rate of interest. In such an ideal loan market, therefore, where every individual could freely borrow or lend, the rates of preference for present over future income for all the different individuals would become equal to each other and to the rate of interest.

§ 3

To illustrate this reasoning by a diagram, let us suppose the income-stream to be represented as in Figure 6, and that the possessor wishes to obtain a small item X’ of immediately ensuing income, for a somewhat larger item X” later on. He therefore modifies his income-stream from ABCD to EBD. But this change will evidently produce a change in his time-preference. If the rate of time-pref-

erence corresponding to the income-stream represented by the unbroken line is 10 per cent., the rate of preference cor-

responding to the broken line will be somewhat less, say

Sc. 3]

FIRST

APPROXIMATION

121

8 per cent. If the market rate of interest is 5 per cent., it is evident that the person will proceed to still further borrowing. By repeating the operation several times he {

Fia. 6.

can evidently produce almost any required conformation in his income-stream. If, instead of borrowing, he wishes to lend (Fig. 7), he surrenders from his present income-

Fic. 7.

stream the amount X’ for the sake of the larger amount X” at a later time. He will engage in the former series of operations if, at the start, his subjective preference for present eatk exceeds the market rate of interest, After and in the latter, if it falls short of that rate.

THE

122

RATE

OF

INTEREST

[Cuap. VII

the operations are completed and the final conformations of the income-streams are determined, the rates of time-

preference are all brought into conformity with the market rate of interest. The loan is effected under the guise of money. We do not confessedly borrow and B ' _ lendincomes, but money. Yet ee ae >~- B’

tual fact he secures the title Fra. 9. to $100 worth of future income —immediately future, perhaps — and parts with the title to $105 worth of income more remotely future.

There are six principal types of individuals in a loan market. In the first type (Fig. 8) the individual is supposed to be possessed of an increasing income-stream AB which in his mind results in a rate of preference above the market rate. This leads

Fra. 10.

-

him to borrow, and relatively

to level up his ascending income-stream to such a position as A’B’. The second type of individual already possesses & uniform income-stream AB

(Fig. 9), but, nevertheless,

being of a spending type, experiences a rate of preference also above the market rate, and will therefore modify his income-stream to the curve A’B’. The third type is represented in Figure 10. This individual has a rate of preference in excess of the market rate, even with a descending

Src. 3]

FIRST

APPROXIMATION

123

curve AB. The consequence is that by borrowing he obtains a curve A’B’ of still steeper descent. The preceding three cases are of borrowers. In like manner there are

types

three

of

bi

lenders. Figure 11 represents a descending type of income AB which, by lending present income in return for future income, is converted into a Fig. 11. relatively uniform income A’B’; Figure 12 represents a uniform income converted, by lending, into an ascending income; and Figure 13 an ascending income converted into a still more steeply ascending income. In all cases we see that the borrowers change their income

curve by tipping it down in the future and up in the present; ye

A

eee

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oa

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whereas the lenders tip their income curves in the opposite direction. Of the three types

of borrowers

and of lenders,

the first in each group of three (see Figs. 8 and 11) is the

usual and normal case. In both these cases the effort is to transform the given income into a more uniform one, the rising curve (Fig. 8) being lowered and the falling curve (Fig. 11) being raised toward a common horizontal position. Figure 10 and Figure 13, on the other hand, represent extreme and unusual UB cases. The former (Fig. 10) y

aa:

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spite of rapidly increasing in- yw Fig. 13. come, saves even more. true that, remains it equation, But whatever the personal curve income his for each individual, the more ascending the higher his rate of preference, and the more descending

124

THE

RATE

OF

INTEREST

[Cuap. VII

the curve, the lower the rate. If the descent is sufficiently rapid, the rate of preference could be made zero or even negative. In these cases, the income is such that its possessor would sacrifice present income to future, even if the market rate of interest were zero.’ These are, of course, not the only types which could be considered, but they are some of the most important. To them we may add the type of fluctuating income, as represented in Figure 14, which may result in alternate bor-

Fia. 14.

rowing and lending so as to produce a more nearly uniform income-stream. It must not be imagined that the classes of borrowers and lenders correspond respectively with the classes of poor and rich. Personal and natural idiosyncracies, early training and acquired habits, accustomed style of living, the usages of the country, and other circumstances discussed in Chapter VI, will, by influencing foresight, selfcontrol, regard for posterity, etc., determine whether a man’s rate of preference is high or low, and therefore whether he becomes a spender or a saver. So far as the character of the income-stream itself tends to place an individual in one or the other of these classes, the nature of the influence is in accordance with the principles stated in Chapter VI in respect to the four features, size, time-shape, composition, and probability. As to size, the larger the

income the more likely, in general, is its possessor to become a lender, because large incomes, in general, reduce the rate of preference for present over future income; as to time+ This is the case mentioned by Carver (Theory of Distribution, pp. 232-236), when he remarks that a man with $100 in his pocket would not think of spending it all on a dinner to-day, but would save at least some of it for to-morrow.

Src. 4]

FIRST

APPROXIMATION

125

shape, ascending incomes are apt to make the possessors borrowers, and descending incomes to make them lenders; as to composition, incomes well endowed with the food element are less apt to make their possessors borrowers than incomes of the contrary type; and as to probability, incomes which are uncertain tend sometimes to make their possessors borrow, sometimes to lend. § 4

But borrowing and lending are not the only ways in which one’s income-stream may be modified. The same result may be accomplished simply by buying and selling property ; for, since property rights are merely rights to particular income-streams, their exchange substitutes one such stream for another of equal value but differing in time-shape, composition, or certainty. This method of modifying one’s incomestream, which we shall call the method of sale, really includes the former method of loan; for a loan contract is at bottom a sale, as Bohm-Bawerk has so clearly shown. That is, it is the exchange of the right to present or immediately

ensuing income for the right to more remote or future income. A borrower is a seller of a note of which the lender is the buyer. A bondholder is regarded indifferently as a lender and as a buyer of property. The concept of a loan may therefore now be dispensed with by being merged in that of sale. By selling some property rights and buying others

it is possible to transform one’s income-stream at will, whether in time-shape, composition, or probability. Thus, if a man buys an orchard, he is providing himself with future income in the use of apples;

if, instead, he buys apples, he

is providing himself with similar but more immediate income. If he buys securities, he is providing himself with future money, convertible when received into true income. If his security is a share in a mine, his incomestream is less lasting, though it should be larger, than if the security is stock in a railway. Purchasing the right to

126

THE

RATE

OF

INTEREST

[Cuap. VII

remote enjoyable income is called investing; to immediate enjoyable income, spending. These, however, are purely relative concepts, for “remote” and “immediate” are relative terms. Buying a winter overcoat or a carpet may be called investing, and on the other hand, buying a factory or a ship may be called spending. And yet the antithesis between “spending” money and “investing” is important; it is the antithesis between immediate and remote income. The adjustment between the two determines the time-shape of

one’s income-stream. Spending increases immediate income but robs the future, whereas investing provides for the future to the detriment of the present. Popular usage has devised many other terms and phrases in this field, most of which, like “spending” and “investing,’ while containing meaning of importance, include also the alloy of misconception. Thus, the phrase “ capital seeking investment”’ means that capitalists have property for which they desire, by, exchange, to substitute other property, the income from which is more remote. It does not mean that the inanimate capital has of itself any power to “seek investment’’; it does not mean that there is any

hard and fast line between invested and uninvested capital. Again, the phrase “saving capital out of income” means “not spending,” —reserving money which would otherwise be spent for immediate enjoyable income in order to exchange it for remoter income; it does not mean the creation of new capital, though it may lead to it. Many needlesscontroversies have centered about the phenomenon of “saving,” chiefly because neither “saving” nor “income” was clearly defined.' From what has been said it is clear that by buying and

selling property an individual may change the conformation ? Thus, by “saving,’”’ some writers understand that capital necesearily increases, and hence the income-stream is made to ascend : others, like Carver (loc, cit. p. 232), apply the term broadly enough to

include the case where a descending income is simply rendered less descending. The latter view harmonizes with that here presented.

Sxc. 5]

FIRST APPROXIMATION ;

127

of his income-stream precisely as though he were specifically lending or borrowing. Thus, if a man’s original incomestream is $1000 this year and $1500 next year, and if, selling this income-stream, he buys with the proceeds

another yielding $1100 this year and $1395 next year, he has not, nominally, borrowed $100 and repaid $105, but — increased he has done what amounts to the same thing , his income-stream of this year by $100 and decreased that of next year by $105, the $100 being the modification produced in his income for the first year by selling his original income-stream and substituting the final one, and $105 being the reverse modification in next year’s income produced by the same operations. The very same diagrams which were used before may be taken to represent these operations. A man sells the income-stream ABCD (Fig. 6) and with the proceeds buys the stream HEBD. The X’ and X” are, as before, $100 and $105, but now appear explicitly as differences in the value of two incomestreams instead of direct loans and returns.

§ 5

In passing we may note that interest-taking cannot be prevented by prohibiting loan contracts. To forbid the particular form of sale called a loan contract would leave possible other forms of sale, and, as was shown in The Nature of Capital and Income, the valuation of every property-right involves interest. If the prohibition

left individuals free to deal in bonds, it is clear that they would be still borrowing and lending, but under the name of “sale”; and if “bonds” were tabooed, they could change

the name to “preferred stock.” It can scarcely be supposed that any prohibition of interest-taking would extend to all buying and selling; but as long as buying and selling of any kind were permitted, the virtual effect of lending and borrowing would be retained. The possessor of a forest of young trees, not being able to mortgage their future

128

THE

RATE

OF

INTEREST

[Cuap. VII

return, and being in need of an income-stream of a less deferred type than that receivable from the forest itself, would simply sell his forest and with the proceeds buy, say, a farm, with a uniform flow of income, or a mine with a decreasing one. On the other hand, the possessor of a capital which is depreciating, that is, which represents an income-stream great now but steadily declining, and who is anxious to “save” instead of “spend,” would sell his depreciating wealth and invest the proceeds in such instruments as the forest already mentioned. It was in such a way, as for instance by “rent purchase,” that the medieval prohibitions of usury were rendered nugatory. Practically, at the worst, the effect of restrictive

laws is simply to hamper and make difficult the finer adjustments of the income-stream, compelling would-be borrowers to sell wealth yielding distant returns instead of mortgaging it, and would-be lenders to buy the same, instead of lending to the present owners. It is conceivable that ‘‘explicit”’ interest might disappear under such restrictions, but “implicit”? interest would remain. The young forest sold for $10,000 would bear this price, as now, because

it is the discounted value and the price of the farm termined in like manner. cases must be the same,

of the estimated future income; bought for $10,000 would be deThe rate of discount in the two because, by buying and selling,

the various parties in the community adjust their rates of preference to a common level, —an implicit rate of interest thus lurking in every contract, though never specifically appearing therein. Interest is too omnipresent a phenomenon to be eradicated by attacking any particular form; nor would any one undertake it who perceived the substance as well as the form.!' In substance, the rate of interest represents the terms on which the earlier and later elements of income-streams are exchangeable. Cf. Fetter, Principles of Economics, New York (Century), 1904,

pp. 134, 135.

Sxc. 6]

FIRST APPROXIMATION

129

§ 6 The fact that, through the loan market, the marginal

rate of time-preference for each individual is made equal to the rate of interest, may be stated in another way, namely, that the total present desirability or utility of the individual income-stream is made a maximum. For, consider again the individual who modifies his original fixed income-stream by borrowing until his rate of preference is brought into unison with the rate of interest. His rate of preference was at first 10 per cent.; that is, in order to secure an addition of $100 to his present income, he was willing to sacrifice $110 of next year’s income. But he only needed to sacrifice $105; that is, he was enabled to get his loan for less than he would have been willing to pay. He was therefore a gainer to the extent of the present deThe second $100 sirability of $5 of next year’s income. borrowed was equivalent, in his present estimation, to $108 of next year’s income, and the same reasoning shows that, as he pays only $105, he saves $3; that is, he adds the present desirability of $3 due next year to the present “‘ total desirability” or “total utility” of his incomestream. In like manner, each successive increment of loans

adds to his present total desirability, so long as he is willing to pay more than $105 of next year’s income for $100 of this year’s income.

But, as he proceeds, his gains

and his eagerness diminish until they cease altogether. At, let us say, the fifth instalment of $100, he finds himself barely willing to pay $105; his present total desirability is then a maximum, and any further loan would decrease it. A sixth $100, for instance, is worth in his estimation less than $105, say $104, and as, in the loan market, he would have to sacrifice $105 next year to secure it, the contracting of such a loan would mean a loss of desirability to the extent of $1 due in one year. Thus, by borrowing up to the point where the rate of preference for present over K

130

THE

RATE

OF INTEREST

[Cuap. VII

future income is equal to the rate of interest, the individual

secures the greatest ‘total desirability.” Similar reasoning, applied to the individual on the other side of the market, whose rate of preference is initially less than the market rate of interest, will show that he also will maximize his present total desirability by lending up to the point where his rate of preference corresponds to the rate of interest. At the beginning, $100 this year has to him the same present desirability as $102 due one year hence, whereas in the market he may secure $105. It is then clear that by lending $100 he gains the present desira-

bility of $3 due one year hence. By lending each successive $100 he will add something to his total present desirability, until his rate of preference for present over future income is raised to a level equal to that of the rate of interest. Beyond that point he would lose by further lending; but at that point he will stop, and his present total desirability will therefore be a maximum.

§ 7 We are now in a position to give a preliminary: answer to the question, What determines the rate of interest? Thus far we have regarded the individual only, and have seen that he conforms his rate of preference to the rate of interest. For him the rate of interest is a relatively fixed fact, since his own time-preference and resulting action can affect it only infinitesimally. His rate of preference is the variable. In short, for him individually the rate of interest is cause, and the rate of preference, effect. For society as a whole, however, the order of cause and effect is reversed. This change is like the corresponding inversion

of cause and effect in the theory of prices. Each individual regards the market price, say, of sugar, as fixed, and adjusts his marginal utility to it; whereas, for the entire group forming the market, we know that the price of sugar is due

Sxc. 7]

FIRST

APPROXIMATION

to its marginal utility to the consumer.’

131

In the same way,

while for the individual the rate of interest determines the rate of preference, for society the rates of preference of the individuals determine the rate of interest. The rate of interest is simply the rate of preference, upon which the whole community may concur in order that the market of loans may be exactly cleared. To put the matter in figures: if the rate of interest is set very high, say 20 per cent., there will be relatively few borrowers and many would-be lenders, so that the total extent to which would-be lenders are willing to reduce their income-streams for the present year for the sake of a much larger future income will be, say, 100 million dollars; whereas, those who are willing to add to their present income at the high price of 20 per cent. interest will borrow only, say, one million. Under such conditions the demand for loans is far short of the supply and the rate of interest will therefore go down. At an interest rate of 10 per cent. the present year’s income offered as loans may be 50 millions, and the amount which would be taken at that rate only 20 millions. There is still an excess of supply over demand, and interest must needs fall further. At 5 per cent. we may suppose the market cleared, borrowers and lenders being willing to take or give respectively 30 millions. In like manner it can be shown that the rate would not fall below this, as in that case it would result in an excess of demand over supply and cause the rate to rise again. Thus, the rate of interest is the common market rate of

preference for present over future income, as determined by the supply and demand of present and future income. Those who, having a high rate of preference, strive to acquire more present income at the cost of future income, tend to raise the rate of interest. These are the borrowers, the 1 See the author’s ‘Mathematical Investigations in the Theory of Value and Prices,’ Transactions of Connecticut Academy, New Haven, 1892, p. 28.

132

THE

RATE

OF

INTEREST

[Cuap. VII

spenders, the sellers of property yielding remote income, such as bonds and stocks. On the other hand, those who, having a low rate of preference, strive to acquire more future income at the cost of present income, tend to lower the rate of interest. These are the lenders, the savers, the investors. The mechanism just described will not only result in a

rate which will clear the market for loans connecting the present with next year, but, applied to exchanges between the present and the remoter future, it will make similar adjustments. While some individuals may wish to exchange this year’s income for next year’s, others wish to exchange this year’s income for that of the year after next, or for a portion of several years’ future incomes. The rates of interest for these various periods are so adjusted as to clear the market for all the periods of time for which contracts are made. If we retain our original assumption that every man is initially endowed with a fixed and certain income-stream which, by borrowing and lending, can be freely bought and sold and thereby redistributed in time, the foregoing discussion gives us a complete theory of the causes which determine the rate of interest, or rather, the rates of interest for various time-periods. These rates of interest would, under these circumstances, be fully determined by the following four conditions, to which all the magnitudes in the problem of interest must conform :— (1) The rate of time-preference of each individual for present income, as compared with remoter income, depends upon the character of his income-stream, as finally modified and determined by the very act of borrowing or lending,

buying or selling. (2) Through the variations in the income-stream produced by loans or sales, the rates of preference for all

individuals in the market are brought into equality with each other and with the market rate of interest. This condition is equivalent to another;

namely, that

Sc. 7]

FIRST APPROXIMATION

133

each individual exchanges present against future income, or vice versa, at the market rate of interest up to the point of maximum desirability. (3) The market rate of interest will be such as will just clear the market; namely, will make the loans and borrow-

ings cancel each other for each period of time. (4) All loans are repaid with interest; that is, the present value of the payments, reckoned at the time of contract, equals the present value of the repayments. More generally, the modifications or departures from a person’s original income-stream effected by buying and selling are such that the algebraic sum of their present values is zero. These four conditions not only determine the rate of interest, but determine also all the other variable elements which enter into the problem; namely, the individual rates of preference (equal to the rate of interest) and the amounts which are borrowed and lent. The formulation of these four determining conditions constitutes our first approximation to the theory of interest. The sufficiency of the four conditions and their coérdination may be made clear by means of the mathematical statement contained in the Appendix to this chapter.

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PART

III.

CHAPTER

VIII.

CHAPTER

IX.

Seconp

anp

Srconp APPROXIMATION

INTEREST CHAPTER

X.

CuHaPTtER

XI.

TuHrrp APPROXIMATIONS

(ASSUMING

TO THE

INCOME

THEORY OF

FLEXIBLE)

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APPROXIMATION

INTEREST

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CHAPTER ROLE

OF

INTEREST

IN

XII ECONOMIC

on CS. ras ae. 64h

THEORY

§1 Havine shown how the rate of interest is determined, we have reached the goal which we have set ourselves in the present book. But, though this goal marks the end of the present inquiry, it is also the starting-point for other economic inquiries of the greatest importance. We cannot attempt in this book to explore the fields which would thus open out, but in the present chapter we shall indicate briefly what they are. ( The rate of interest plays a central réle in two great branches of economic science, — the theory of prices, and the theory of distribution. The rdéle of the rate of interest in the theory of prices applies to the determination of the price of wealth, property, and services. } As was shown in The Nature of Capital and Income, the price of any article of wealth or property is equal to the discounted value of its expected future services. If the value of these services remains the same, a rise or fall in the rate of interest will consequently cause a fall or rise respectively in the value of all instruments of wealth. The extent of this fall or rise will be the greater the further into the future the services of wealth extend.’ Thus, land, from which services are expected to accrue uniformly and forever, will be doubled in value if the rate of interest is halved, or halved in value if the rate of interest is doubled. In the case of dwellings, however, the life of which is limited, if the rate of interest is doubled, the price of 1 See The Nature of Capital and Income, Chap. XIII. Q

225

226

THE

RATE

OF

INTEREST

(Caar. XII

dwellings will fall less than half, and if the rate

of

interest is halved, the price of dwellings will rise to less than double. In the case of furniture the fluctuations in

value will be even less extensive, and so through the list of less durable commodities, such as clothing, to those of very perishable types, such as food, the value of which will not be sensibly affected by a variation in the rate of interest. § 2

As to the influence of the rate of interest on the price of services, we first observe that services may be intermediate or final! The value of intermediate services or ‘‘interactions” is derived from the succeeding future services to which they respectively lead. For instance, the value

to a farmer of the services of his land in affording pasture for sheep will depend upon the discounted value of the services of the flock in producing wool. If he rents the land, he will calculate what he can afford to pay for it on the basis of the value of the wool which he would expect to obtain from his flock. In like manner, the value of the

wool-output to the woolen manufacturer is in turn influenced by the discounted value of the output of woolen cloth to which it contributes. In the next stage, the value of the production of woolen cloth will depend upon the discounted value of the income from the production of woolen clothing. Finally, the value of the last named will depend upon the expected income which the clothing will

bring to those who wear it, — in other words, upon the use of the clothes. Thus the final services, consisting of the use of the clothes, will have an influence on the value of all the anterior services of tailoring, manufacturing cloth, producing wool, and pasturing sheep, while each of these anterior services, +See The Nature of Capital and Income, Chap. IX. The subject has already been referred to in the present volume, Chap. VIII.

Sxc.2]

ROLE

OF

INTEREST

IN ECONOMIC

THEORY

227

when discounted, will give the value of the respective capital which yields them; namely, the clothes, cloth, wool, sheep, and pasture. We find, therefore, that not only all articles of wealth, but also all the intermediate services (“‘interactions”) which they render, are dependent upon final enjoyable uses, and are linked to these final uses by the rate of interest. If the rate of interest rises or falls, this chain will shrink or expand. The chain hangs, so to speak, from its final link of enjoyable services, and its shrinkage or expansion will therefore be most felt by the links most distant from these final services. A change in the rate of interest will affect but slightly the price of making clothing, but it will affect considerably the price of pasturing sheep. A study, therefore, of the theory of prices involves (1)

a study of the laws which determine the final services on which the prices of anterior interactions depend; (2) a study of the prices of these anterior interactions, as dependent, through the rate of interest, on the final services; (3) a study of the price of capital instruments and capital property as dependent, through the rate of interest, upon the prices of their services. The first study, which seeks merely to determine the laws regulating the price of final services, is relatively independent of the rate of interest. The second and third, which seek to show the dependence on final services of the anterior services and of the capitals which bear them, involve and depend upon the rate of interest. Under this second study will fall, as a special case, the study of the determination of economic rent, both the rent of land and the rent of other instruments of wealth. Thus, the rent of the pasture referred to, consist-

ing, as it does, of the value of the services of pasturing, is dependent, through the rate of interest, upon the discounted value of the future final services to which the land contributes.

ment.

It is clear, then,

that the rent of the land

228

THE

RATE

OF

INTEREST

[CHap. XII

§3 Similar considerations apply to the determination of the rate of wages. So far as the employer is concerned, the payment of wages to a workman represents the value of

his services. These services are interactions or intermediate services leading to some future enjoyable service. Thus, the shepherd hired by the farmer to tend the sheep in the pasture renders services the value of which to the farmer is estimated in precisely the same way as the value of the services of the land which he hires. It follows that the rate of wages is dependent upon the rate of interest, and, conformably to the previous reasoning, the dependence of wages on the rate of interest is the more pronounced the more remote are the ultimate services to which the work of the laborer leads. As stated in Chapter IX, in a community where the workmen are largely employed in enterprises requiring a long time, such as digging tunnels and constructing other great engineering works, the rate of wages will tend to fall appreciably with a rise in the rate of interest, and to rise appreciably with a fall in the rate of interest; whereas in a country where the laborers are largely engaged in personal services or in other work which is not far distant from the final goal of enjoyable services, a change in the rate of interest will affect the rate of wages but slightly. What has been said, however, applies only to wages from the standpoint of the employer. The rate of wages is dependent upon supply as well as demand; that is, upon the willingness of the workman to offer his services, as well as upon the desire of the employer to secure them. From the standpoint of the laborer, wages constitute an incentive to exertion or labor. This exertion is, as we have seen, a final disservice, and its value is not determined by the rate of interest in the manner of services which are intermediate. It is a great mistake to treat the subject of wages, as many authors do, exclusively from the employer’s standpoint.

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Our purpose here, however, is not to enter into an extended discussion of the theory of wages, but merely to show at

what points in that theory the rate of interest enters, and at what points it does not enter. § 4

The second great branch of economics to which the rate of interest applies is the theory of distribution. In the classical political economy, the relation of the rate of interest to distribution was entirely misconceived. Distribution was erroneously regarded as a separation of the income of society into ‘interest, rent, wages, and profits.”’ By “‘interest”’ of course was meant, not the rate of interest, but the rate of interest multiplied by the value of the capital “yielding interest.’”” But we have seen that the value of the capital is found by taking the income which it yields and capitalizing it by means of the rate of interest. To reverse this process, and obtain the income by multiplying the capital by the rate of interest, is proceeding in a circle. The result of multiplying capital by the rate of interest, 1.€. income, is not really a complex product of two factors, but, on the contrary, is the single original factor, —income. We have seen in this book that it is this income which affords the basis for the determination of the rate of interest, and, through the rate of interest, of capital value. The income-stream of society is the ultimate and basic fact from which the whole economic fabric should be constructed. All of this income springs from capital-wealth, if land and man are included in that term, or if not, from capital and man, or capital, land, and man. It may all be capitalized, and hence, if we follow the definition of capital adopted in this book, it may all be regarded as interest upon the capitalvalue thus found. Hence “‘interest”’ is not a part, but the whole, of income. It includes what is called rentand profits, and even wages; for the income of the workman may

be capitalized quite as truly as the income of land or

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Thus, so far from having ‘“‘interest, rent, machinery. wages, and profits” as mutually exclusive portions of income, we see that “interest” includes all four. The error of the classical economists and of their modern followers in distinguishing between interest, rent, etc., as separate but codrdinate incomes, is partly due to the failure to perceive that whereas all income springs from capitalwealth, yet capital-value springs from income. Another oversight closely associated with the last is that by which rent and wages were conceived as determined independently of the rate of interest, whereas we have

just seen that the rate of interest enters as a vital element into the determination of both.

We shall, therefore, in discussing the theory of distribution, abandon the “classical” point of view entirely. And little regret should be caused by such abandonment, for the concept of distribution which the classical economists have given us is quite incompatible with the ordinary conception of the term. The phrase ‘‘distribution of wealth”’ implies ordinarily, or should imply, the problem of the relative wealth of individuals, — the problem of the rich and the poor. But the separation of the aggregate income into four abstract magnitudes has little to do with the question

of how much income the different individuals in society receive. Were it true that society consisted of four independent and mutually exclusive groups, — laborers, landlords, entrepreneurs and capitalists, — the fourfold defi-

nition would have some connection with the actual distribution of wealth. But, in fact, the entrepreneur is almost invariably a ‘‘capitalist”’; 7.e. is the owner of other capital than land; the “capitalist”’ is frequently a landlord, or vice versa; and even the laborer is to-day often a small

capitalist. It is true that a century ago in England the lines of social classification corresponded roughly and to some extent, at least, with the abstract divisions into which + Cf. Edwin Cannan, “‘ The Division of Income,” Quarterly Journal of Economics, May, 1905.

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economists separated income; but this fact is of interest only in explaining historically the origin of the classical theory of distribution. §5

Turning to the true problem of distribution, that of determining the amounts of capital and income possessed by different individuals in society, we find that economists have contributed extremely little to its solution. A

statistical beginning has been made by Professor Pareto in his interesting ‘curves of distribution of income,” ? in which he shows the surprising result that in all cases where figures are available, the relative distribution of incomes is fairly uniform in different times and places. So far as the philosophical theory of distribution is concerned, the only writer who seems to have contributed materially to the subject is John Rae.* He showed that persons who had naturally what we have called in this book a low rate of preference for present over future income tended to grow rich, whereas those who had the opposite trait tended to grow poor. We saw in a previous chapter that the rates of prefer-

ence among different individuals were equalized by borrowing and lending or buying and selling. In the case of an individual whose rate of preference for present enjoyment was unduly high, we found that he would contrive to modify his income-stream by increasing it in the present at the expense of the future. We were then intent on studying this phenomenon only on the side of income; but the effect on capital can be easily seen by applying the principles of

The Nature of Capital and Income, Chapter XIV. If a modification of the income-stream is such as to make the present rate of realized income exceed the “standard” Cf. Edwin Cannan, loc. cit. 2 Cours d’Economie Politique, Vol. II, Lausanne, 1897, Book III. ° The Sociological Theory of Capital, Chap. XIII.

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income, capital must be depleted to the extent of the excess, and the individual will grow poor. This may be brought about by borrowing immediate income and paying future income, or by selling those instruments the income of which is far distant, and buying those which have more immediate returns. Individuals of the type of Rip Van Winkle, if in possession of land and other durable instruments, will either sell or mortgage them in order to secure the means for obtaining enjoyable services more rapidly. The effect will be, for society as a whole, that those individuals who have an abnormally low appreciation of the future and its needs will gradually part with the more durable instruments, and that these will tend to gravitate into the hands of those who have the opposite trait. By this transfer an inequality in the distribution of capital is gradually effected, and this inequality, once achieved, tends to perpetuate itself. The poorer a man grows the more keen his appreciation of present goods is likely to become. When once the spendthrift is on the downward road, he is likely to continue

in the same direction.

When he has succeeded in losing

all his capital except his own person, the process usually comes to an end, because society, in self-protection, decrees

that it shall go no further.

But where there is no such

safeguard, the unfortunate victim may sink into even lower

stages of debt servitude, as in Java‘ or Russia. Reversely, when the accumulator is well advanced in his accumulations, his rate of preference for the present diminishes still further, and accumulation becomes still easier. Hence, in some countries the rich and poor come to be widely and permanently separated, the former constituting a hereditary aristocracy and the latter a helpless and degraded peasantry.

Fortunately, however, another factor enters which tends to counteract these tendencies. This is the effect of habit. It has already been noted that one’s rate of preference for +See Prof. Clive Day, The Dutch in Java, New York (Macmillan), 1904, Chap. X.

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present over future income, given a certain income-stream, will be high or low according to the past habits of the individual. If he has been accustomed to simple and inexpensive ways he finds it fairly easy to save and ultimately accumulate a little property. The habitsof thrift being transmitted to the next generation result in still further accumulation, until, in the case of some of the descendants, affluence or great wealth may result. Reversely, if a man has been brought up in the lap of luxury he will have a keener desire for present enjoyment than if he had been accustomed to the simple living of the poor. The effect of this factor is that the children of the rich, who have been accustomed to luxurious living and who have inherited only a fraction of their parents’ means, will, in attempting to keep up the former pace, be compelled to check the accumulation and even to start the opposite process of the dissipation of their family fortune. In the next generation this reverse movement is likely to gather headway and to continue until, with the gradual subdivision of the fortune and the increasing reluctance of the successive generations to curtail their expenses, in the third or fourth generation It thus often there comes a return to actual poverty.

happens that there is a tendency for the accumulation and dissipation of wealth to occur in cycles. If there is the conjunction of favorable circumstances, as thrift, ability,

and good fortune, a few individuals will rise from the lower ranks. They accumulate a few thousand dollars, which, under like favoring circumstances, in the next generation or two may become several millions. Then the unfavorable effects of luxury begin, and in an equal num-

ber of generations the majority of the heirs have returned to the level at which their ancestors began. An old adage has stated this observation in the form, ‘‘ From shirt sleeves to shirt sleeves in four generations.” This cyclical move-

ment is more apt to occur in countries like the United States, where, owing to the rapidly changing conditions, there is a larger number of opportunities either for rising

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or falling in the economic scale. Where, as in the older countries of Europe, conditions have become fixed and less favorable

to changes of any kind, the tendency of the

distribution of wealth is to remain relatively unchanged. This is especially true where, as in England, the customs as to the inheritance of property have tended to keep large fortunes intact in the hands of the eldest son. §6 In the general causation of distribution which has thus been outlined, the central réle is played by the individual rate of preference for present over future income, which, as we have seen, is the subjective prototype of the rate of interest. The study of the theory of interest, therefore, lays the foundation for a study of the theory of distribution. The objective rate of interest represents the norm to which the individual adjusts his rate of preference for present over future income, and in this adjustment he changes his economic status for better or worse. The existence of this general market rate of interest to which he adjusts his rate of preference supplies an easy highway for the movement of his fortune in one direction or the other. If an individual has spendthrift tendencies, their indulgence is facilitated by access to a loan market; and reversely, if he desires to save, he may do so the more easily if there is a market for savings. The irregularities in the distribution of capital are thus due to the opportunity to effect exchanges of parts of the income-stream separated in time. The rate of interest is simply the market price for such exchange. By means

of this market price, both those who wish to

barter present for future income and those who wish to do the reverse, may satisfy their desires. The one will gradually increase, and the other decrease, his capital. If all individuals were hermits, it would be much more difficult either to accumulate or to dissipate fortunes, and the distribution of wealth would therefore be much more even.

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Inequality arises out of the exchange of income, carrying some individuals toward wealth and others toward poverty. The inequality of wealth is facilitated by the existence of a loan market. In a sense, then, it is true, as the socialist maintains, that inequality is due to social arrangements; but the arrangements to which it is due are not, as he assumes, primarily such as take away the opportunity to rise in the economic scale; they are the contrary arrangements which facilitate both rising and falling, according to the choice of the individual. The improvident sink like lead to the bottom. Once there, they or their children find difficulty in rising. Accumulation is a slow process, and especially slow when the great numbers of the poor have, by competition, reduced the values of their services so low that the initial saving becomes almost impossible.

This is not the place for following out these tendencies and their sociological effects, nor need we stop to answer the many questions which arise in such an inquiry, such as, What is the effect of a change in the rate of interest in stimulating or discouraging the accumulation or dissipation of capital?+ Or, What is the effect on the poor of the luxurious habits of the rich? Nor are we concerned with the other factors which influence the distribution of wealth, but which do not involve the rate of interest. We are at present content merely to prepare the way for their answer by indicating the nature of the problems and the relation of the theory of interest to them. 1 See E. C. K. Gonner, Interest and 1906.

Saving, London (Macmillan),

CHAPTER APPLICATION

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§ 1

WE have now completed the formal statement of our theory of interest. It remains to show in what way this theory may be brought into connection with actual experience. For this purpose we need first to classify the various forms which interest takes. We have seen that the rate of interest discloses itself in two ways; namely, as explicit and implicit interest.

We begin with explicit interest, or the interest in a loan contract. From the standpoint of the borrower, loan contracts may be classified as follows :— f

reine

To offset misfortune or improvidence. For private |To offset fluctuations in income and outgo. purposes | To anticipate improvement in financial condition. For public For military purposes. purposes To offset fluctuations in revenue and ex(municipal, penses. etc.) For public improvements. Sire ae Crop liens. 4. |Commercial paper. periodic f loahe Accommodation paper. Call loans. For business purposes

Mortgages Mortgages

Long or per-

l

L

estate.

on farms. on city real

manent loans \Mortgage bonds of corporations. Debentures of corporations.

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Private loans are loans of individuals for personal purposes other than those arising out of business relations. Of these, loans contracted because of misfortune or improvidence, though to-day constituting a very small fraction of total indebtedness, represent probably the original type of loan. It was against such loans that the biblical, classical, and medizval prohibitions and regulations were directed, and it is only against them to-day that, in enlightened communities, regulations affecting the rate of interest still survive. It is such loans that supply most of the business to pawn shops, the patrons of which are usually victims of misfortune or improvidence. It is clear that the theory

of interest which has been propounded applies to this species of loan. Sickness or death in one’s family, or losses from fire, theft, flood, shipwreck, or other causes, make temporary inroads upon one’s income. It is to tide over

such a stringency in income that the loan is contracted. It ekes out the less adequate income of the present by

sacrificing something from the more adequate income expected in the future. Similar principles apply to the spendthrift, who, though not a victim of accidental misfortune,

brings misfortune upon himself.

He borrows in order to

supplement an income inadequate to meet the requirements which he has set himself, while he trusts for repayment to the shadowy resources of a distant future. It is evident, therefore, that the loans just described are made for the sake of correcting an income curve the time-shape of which is inconvenient or intolerable. The second class of personal loans comprises those growing out of such fluctuations in income as are not due to misfortune or improvidence. Many persons receive their money-income in very irregular and unequal instalments, while their money outgo may likewise have an irregular time-schedule. Unless the two sides of the account happen to synchronize, the individual will be alternately “short” and ‘flush.’ Thus, if he receives his largest dividends in January, but has to meet his largest expenses, let us say

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taxes, in September, he is likely to borrow at tax time for the ensuing four months, in anticipation of the January dividends. That is, he borrows at a time when his incomestream would otherwise be low, and repays at a time when it would otherwise be high. The effect is to level up the fluctuations of his income. The third class of personal loans comprises those which grow out of large expected additions to income. Heirs to a fortune sometimes borrow in anticipation of their bequests. A considerable volume of such loans has undoubtedly been contracted, especially in Great Britain. The borrower in this case is evidently trying to enjoy in the present some of the income which is promised for the future; in other words, to alter the time-shape of his income-stream in accordance with his desires. The same motives actuate young men preparing for life, and explain the loans which are often contracted by them for defraying the expenses of education. It was for, such persons that Benjamin Franklin left his peculiar bequests to the cities of Philadelphia and Boston in 1790. To each he bequeathed £1000 to be lent out in small sums at 5 per cent. to young married “artificers.”” The sums repaid were to be added to the fund and again lent.

§2 In the case of public loans, we find the same general principles in operation which we have just seen to apply to private loans. By a public loan is meant a loan contracted by a public corporation or association, such as a state, county, municipality, school district, or other administrative

unit, as well as such quasi-public institutions as churches, hospitals, and public libraries. Public loans may be subdivided into three classes: (1) those growing out of military

exigencies; (2) those growing out of fluctuations in income; (3) those growing out of need for public improvements. The first class, loans for war and war preparation, corresponds to the case first considered under private loans, —

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loans growing out of misfortune. Ordinarily the expenses of government are defrayed out of taxes, which constitute a regular deduction from the incomes of the taxpayers; but war brings with it extraordinary expenses which must be met by extraordinary means. If the cost of war were wholly defrayed by taxes, the taxpayers would suffer large and sudden reductions in their incomes for the time being. They prefer instead to place some of the burden on the future, —even upon posterity. This is accomplished by war loans, to be repaid many years after the war is over. Thus, so far as the taxpayers are concerned, the expense of the war is spread over a considerable time, and the immediate reduction in their income-stream, which would otherwise be caused by the war, is avoided. But for the world as a whole this is not true; for others than the taxpayers, namely, the bondholders, must bear the brunt of the reduction in the world’s income-stream which the war has brought about. It follows that the issue of bonds has as its ultimate effect, not a postponement of the cost of the war, but its shifting from one class to another. We thus see that war loans clearly exemplify the theory of loans which has been elaborated. The need for such loans grows out of an impending depression in the income-stream of the taxpayers. The second class of public loans, namely, loans due to fluctuations in public receipts and disbursements, corresponds to the second class of private loans. A government receives its income chiefly in taxes, and only once a year, whereas its outgo occurs day by day and month by month.

It thus happens that a government is alternately accumulating a large surplus and suffering a large deficit. The inconvenient effects of this have been often commented upon, especially in this country, where the Treasury for half a century has been relatively independent of institutions of credit. This inconvenience may be largely avoided by 1 See David Kinley, The Independent Treasury of the United States, Boston (Crowell), 1893.

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a business relation between the government and some institutions of credit, as, for instance, in England, between the government and the Bank of England. The government may correct the irregularities in its income-stream either by borrowing for current expenses in anticipation of taxes, or by lending at interest; that is, depositing the taxes when first received, in anticipation of the expenses which follow. The third class of public loans comprises those for public improvements, such as the erection of government buildings, the improvement of roads, bridges, and harbors, the construction of municipal waterworks or schoolhouses, or the prosecution of other government enterprises. In all

such cases it is usual to finance the enterprise by issuing bonds. The reason clearly is that these improvements constitute an extraordinary cost, similar to the expense of a war, which, without the issue of bonds, would cause a temporary depression inincome-streams. The taxpayers as a whole cannot afford the first heavy drain, even with the prospect of substantial benefits to follow. They therefore prefer, in place of such a fluctuating incomestream, a more uniform one. To secure this uniformity is evidently the purpose of the loan. We see, therefore, that this class of loans also exemplifies the theory of the relation of borrowing and lending to the time-shape of an income-stream.

§3 The third and last general class of loans is that of business loans. Business loans are loans growing out of trade. They are commonly, though not very felicitously, called “productive loans,” whereas the loans which have thus far been considered would commonly be called ‘consumption loans.”” Business loans constitute by far the most important class of present indebtedness. Mr. George K. Holmes has estimated that at least nine tenths of the existing in-

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debtedness in the United States was incurred for the acquirement of the more durable kinds of property, leaving not more than one tenth, and probably much less, as a “consumption debt,” or a debt necessitated by misfortune. No theory of interest would therefore be complete which should fail to apply to business loans. At first sight it would seem that the theory which has

been given, depending as it does on the enjoyable incomestream of an individual, can apply only to consumption loans. Net income, as was shown elsewhere,’ consists of one’s personal satisfactions, — nourishment, clothing, shelter, and other enjoyable services. The loans of business seem too impersonal to be explained by a theory which depends wholly on personal satisfactions. In fact, it has often been said by economists, in treating this subject, that consumption loans are explained on quite other

principles

than loans

contracted

in the regular course

of commercial transactions. Even Bohm-Bawerk, in his Positive Theory of Capital, states that consumption loans are explained by the preference for present enjoyment over future, but that the loans of business are chiefly due to the “technical superiority of present goods,” which grows out of the greater productiveness of lengthy pro-

cesses. A little consideration will show, however, that business loans are not so different from consumption loans; that they also are used to tide over lean times in anticipation of prosperity; and that they are contracted to rectify the distortion of the income-stream which would otherwise result

from business operations. The truth is—and it should never be lost sight of — that business men conduct their business with an eye always to enjoyable income. This is the object of all their operations, though it may be obscured by the interposition of the many intermediate steps, or “interactions.” Business operations are not ends in themselves, but means for ultimate personal enjoyment. 1 The Nature of Capital and Income, Chaps. IX, X. R

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A business man not only conducts his business for what he can get out of it for personal use, but also regulates it so that what thus comes out may accrue not in irregular spurts, but so far as possible in such a stream as will synchronize with the exigencies of his home life. In a sense we may say, therefore, that it is his home that “runs” his

business rather than his business that ‘‘runs”’ his home. § 4

In order to see how the theory of interest which has been explained applies to business loans, let us consider the two chief classes; namely, short loans, or those growing out of periodic variations, and long loans, or those for relatively permanent investment. The short or periodic loans are those which grow out of the change in the seasons and the ebb and flow of business. These loans are obtained usually but once a year at a specified time. The ultimate cause is the cyclical change in the position of the earth in reference to the sun. This gives rise to the cycle of the

seasons, the effects of which are felt not only in agriculture, but in manufacturing, transportation, trade, and banking.

The alternate congestion and thinning of the freight business, the alternate stocking and depletion of raw material in factories, the fluctuations of trade activity, both wholesale and retail, the transfer of bank deposits between New York and the West for ‘moving crops” or for other uses, all testify to the seasonal rhythm which is constantly

felt in the great network of business operations. Without some compensating apparatus such as that for borrowing and lending, these seasonal fluctuations would transmit themselves to the final enjoyable income-streams of individuals, and those incomes, instead of constituting an even flow, would accrue by fits and starts, a summer of lavish enjoyment being followed by a winter on short rations.

To show how borrowing and lending compensate for

these fluctuations, we may consider first what is perhaps

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the most primitive type of the short or periodic loan; namely, that contracted by poor farmers in anticipation of crops. In the South among the negroes this takes the form of what is called a “crop lien,” the cultivator borrow-

ing money enough to enable him to live until crop time and pledging repayment from the crop. Here, evidently, the purpose of the loan is to eke actual enjoyments. The loan, sistence. This case, therefore, interest which has been given. We proceed now to show that applies also to loans contracted

out the meager income of in other words, is for subis covered by the theory of

this same theory of interest in the commercial world at large. A short-time commercial loan is contracted for the purpose of buying goods, with the expectation of repayment after their sale. A common form is what is called ‘commercial paper.’”’ A ready-made clothing house may buy overcoats in summer in order to sell them in the fall. If these operations were conducted on a strictly cash basis, the tendency would be for the income of the clothier to suffer great fluctuations. He could realize but little during the summer, on account of the enormous expense of stock-

ing-in for fall trade, whereas in the fall he could obtain large returns and live on a more elaborate scale. This would mean the alternation of famine and feast in his family. One way to avoid such a result would be to keep on hand a large supply of cash as a buffer between the money-income and personal expenditure. In this case the fluctuations would not reach the stage of personal enjoyment, but would spend their force in fluctuations of the volume of cash. A more effective and less wasteful method for the merchant, of taking the kinks out of his income, is by negotiating commercial paper. The clothier, instead of suffering the large cash expense of stocking-in in summer, will make out a note to the manufacturer of overcoats. After the fall trade, this note is extinguished, having fulfilled its function of leveling the income-stream of the clothier.

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Sometimes merchants contract short-time or periodic loans, not for some specific transaction such as the purchase of stock in trade, but for general business purposes, as, for instance, improvement or enlargement. In this case, the extraordinary expense involved may be met by a species of loan called ‘accommodation paper.” Evidently its function is precisely the same; namely, to rectify the timeshape of the income-stream. In Wall Street and other speculative centers a type of loan known as the “call loan” is common, subject to redemption at the pleasure of the lender, and used by the speculator for the purchase of securities. The speculator borrows when he wishes to buy, and repays when he has sold; and by adroitly arranging his loans prevents the sudden draining or flushing of his income-stream which these purchases and sales would otherwise involve. In all the cases which have been described, the loan grows out of a purchase or group of purchases; and since the tendency of every purchase is to decrease one’s income, and of every sale to increase it, it is clear that loans contracted

for a purchase and extinguished by a sale have as their function the obliteration of these decreases and increases of the income-stream. It is clear, therefore, that these commercial loans fit into the theory of interest which has been propounded. §5 The second class of business loans is that of long-time

loans or ‘‘permanent”’ investments.

In this class are placed

mortgages, whether on farms or on urban real estate.

As

shown by Mr. George K. Holmes of the United States Census, more than two thirds of farm mortgages are contracted for the purchase of the property, and the remainder principally for improving it, or for the purchase of farm implements and other durable wealth or property. These purchases or improvements, involving as they do large expenditures,

would be difficult or impossible without loans. If the attempt

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were made to enter into them without recourse to a loan market, they would cause temporary depressions in the incomestreams of the farmers. The farmer who attempted to buy his farm without a loan would have to cut down his current expenses to a minimum and suffer a corresponding reduction in his enjoyable income-stream, unless he avoided this result by some other of the methods which have been explained, such as “the method of buying and selling.” For instance, he may sell some other capital in order to buy his farm. Mortgages on city lots are usually for the purpose of improving the property by erecting buildings upon it. Here, again, the expense involved would, if taken out of income, reduce the income of the owner temporarily to very small proportions. He naturally prefers to compensate for such extraordinary inroads by a mortgage which defers this expense to the future, when his receipts will be more adequate to meet it. We come next to the loans of business corporations and firms, such, for instance, as railroad bondsand debentures, the securities of street railroads, telegraph, and telephone comThese loans are usually panies, and other ‘‘industrials.” issued for construction purposes, as in cases in which a railroad wishes to extend its lines, replace iron rails with steel ones, or a curved route bya straighter one. The borrowers They may be said in this case are the stockholders. to contract the loan in order not to have the expenses of the improvement taken out of their dividends. Sometimes, where the dividends are large and the stockholders few, dividends are applied, in part or wholly, to the making of improvements. But ordinarily thereduction in thestockholder’s income-stream is avoided by the device of inviting the bondholders to cancel the outgoes connected with the improvement, in consideration of receiving a part of the increased income which will later follow from these improvements. §6

We see, therefore, that business loans, or loans growing out of a purchase and sale, are as truly for the purpose of

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reshaping the income-streams as are private and public loans.

The reasons that business

loans

are usually re-

garded by economists as on a different footing from private and public loans appear to be three :— 1. The proceeds of business loans are usually spent, not

for the borrower’s bread and butter, but for durable capital; consequently the loan seems not to be connected with income, but rather with capital. A spendthrift who borrows $1000 in order to pay for wines is certainly

to be distinguished from a merchant who borrows the same sum in order to pay for new stock in trade. Yet in either case the loan adds $1000 to immediate income beyond what the income would have been without the loan but with the expense for the wines or the stock in trade. To make the comparison as simple as possible, let us suppose that the two men were each enjoying an income of $10,000 a year. This represents the value of their nourishment, clothing, shelter, etc., which constitute true income. In the year (say 1901) of the proposed loan, each man has two courses open to him: (1) he may meet the expenditure for wines or stock in trade by sacrificing one-tenth of his $10,000 worth of nourishment, clothing, shelter, etc., or (2) he may meet it by borrowing. If the spendthrift follows the first course and meets the expenditure by skimping out of his $10,000 income, he will not suffer any change in the value of his income, but will obtain $1000 worth of wine drinking, at a sacrifice of $1000 worth of other pleasures. His income for the year 1901 will still be $10,000. Nor will

there be any necessary change in the income of subsequent years. He merely changes the composition of this year’s enjoyable income partly into wine-drinking, but his income

remains $10,000 a year, The merchant, however, who skimps out of his $10,000 income in 1901 in order to pay for stock in trade, will actually reduce his enjoyed income of 1901 by $1000; for this stock in trade, unlike wine, will not give any immediate satisfaction. It serves only as a means of securing future satisfactions, so that, let us say,

Sxc. 6]

APPLICATION

TO ACTUAL

$1100 may be enjoyed in 1902.

CONDITIONS

247

The income of the mer-

chant will thus be, not $10,000 each year, as was that of the spendthrift, but $9000 in 1901 and $11,100 in 1902.

Having seen what effect the expenditures would have in

the two cases without recourse to borrowing, we next ask what will be the effect in the two cases of borrowing $1000

in 1901 and repaying, let us say, $1050 in 1902. The spendthrift who borrows to get his $1000 worth of wine will have, in 1901, that much more of enjoyed income, making a total enjoyed income in that year of $11,000, and in 1902, when called upon to pay his debt of $1050, he will have to sacrifice just so much out of his income of $10,000 for 1902. His resulting enjoyed income will therefore be in 1902 only

$8950. As to the merchant, he will be able to buy his stock in trade in 1901 without the necessity of any sacrifice out of his $10,000 for that year, so that his income in 1901 will be $10,000. In the following year he will pay the (Of the $1050 for his loan out of the $11,100 for 1902. $11,100, $10,000 was the original income, and $1100 what we have assumed to be the returns from his stock in trade.) He will thus have $10,050 left as his real income for that year.

Comparisons are shown in the following tables:— WHO

INCOME OF SPENDTHRIFT BUYS $1000 WORTH OF WINE 1901

- + ......Without loan ree es ee With loane) ee

WHO

$10,000 | $10,000 8,950 11,000

«|

ee

ae

ea

ee

2 Se

BUYS

-

INCOME OF MERCHANT $1000 WORTH OF STOCK

IN

1901

Withoutiloaime..«

ie

eee)

6

«os

WUE

2

AO

ses

e AL

1902

|

eee

TRADE 1902

9,000 | $11,100

0000" |” 10,050

I S3SsS S390 esssssssssSsSsSsSsSsSsSSSsSsS3 ee

248

THE

RATE

OF INTEREST

[Cuar. XIII

It is clear that in each case the effect of the loan is to add $1000 to the income of 1901 and subtract $1050 from that ‘There is absolutely no difference between the of 1902. two men in this respect. The difference between them is chiefly that the spendthrift is making a foolish and the merchant a wise addition to his income of 1901 at the expense of that of the year following, and this difference is only one of degree, due to the fact that the final satisfactions by means of the wine come earlier than the satisfactions obtained by means of the stock in trade. 2. But the example given of the “‘consumption”’-loan is not the only one possible, and no doubt it will still seem to some readers that there must be another difference between production- and consumption-loans. Suppose the case of a victim of misfortune, such as illness. To tide him over his emergencies he is compelled to borrow, using the proceeds of his loan merely to meet his grocer’s and butcher’s bills. Here is indeed a case of a “‘consumption’’-loan which is not foolish, and yet is surely different from the loan of the merchant to buy stock in trade. The effect of business loans is to enable a merchant to embark on an enterprise, while personal loans merely relieve needs. Let us examine this difference. It is not a difference which invalidates the principle that both loans are additions to present income at the expense of future income. The unfortunate, with his misfortune, but without his loan, would have, let us say, an income of $9,000 in 1901 and $11,100 in 1902, which are the same figures we assumed for the merchant with his investment but without his loan. With the loan, therefore, the unfortunate and the merchant would be in the same situation.

Both would have $10,000

in 1901 and $10,050 in 1902. The effect of the loan in the two cases is thus identical so far as their income-streams are concerned. The difference is that the unfortunate, if deprived of his loan, could not escape from his incomestream of $9,000 in 1901 and $11,100 in 1902, whereas the merchant, if deprived of his loan, could, if he chose, give

Src. 6]

APPLICATION

TO

ACTUAL

CONDITIONS

up the investment in new stock altogether.

249

If the merchant

did not have this option, the two cases would be so similar that not even a stickler for the distinction between consumption-loan and productive-loan would assert any essential difference. For, suppose the merchant has already

been committed, sometime previously, to buy the goods for his stock in trade, not, perhaps, realizing that he would be unable to pay for them without borrowing or skimping. When the time arrives that he must of-necessity buy the goods and pay for them, he finds that a loan is badly needed

to avoid pinching himself in income. He will now think of the loan, not as enabling him to buy stock in trade, for that must be done anyway, but as enabling him to buy his bread and butter. In short, his loan, like the unfortunate’s, is a necessity-loan. It is because ordinarily the merchant is not thus constrained to buy the goods that the loan is connected, in his mind, with their purchase rather than with his private necessities. It still serves to relieve that income, but he has another method of relief, — not to buy the goods at all. The contrast, then, between him and the unfortunate is simply that he has a third possible course which the latter does not have. This is

shown in the following tables :— INCOME

OF MERCHANT 1901

A Without loan and without investment B Without loan but with investment . C With loan and with investment . .

INCOME

OF

1902

. | $10,000 | $10,000 11,100 9,000 . 10,050 10,000 .

UNFORTUNATE 1902

ee loa i toe Be Without oe Sees 28s CaWal loan

tse ees.

es | 8 e000 10,000

$11,100 10,050

250

THE

RATE

OF INTEREST

(Cuap. XIIT

We see here that the unfortunate has two options, B and C, and the merchant three possible options, A, B, and C.

It is the existence of this third option A which makes the chief real difference between the merchant borrower and the borrower in misfortune. So far as the other two options are concerned, the two men are similarly situated. That this fact is overlooked is due to the unconscious substitution, in considering the case of the merchant, of the third option, A, for the second, B. That is to say, when the effect of a merchant’s loan is considered, this effect is measured with reference to his situation without the loan and

without the purchase of the goods, instead of with reference to his situation without the loan but with the purchase. The latter method measures the effect of the loan in the sense that it shows the difference produced by its presence or absence, other things being equal. It treats the merchant’s loan in the same way that the unfortunate’s loan is treated, and thus puts the two on the same basis. The true sequence of thought then is: Of the two options A and B, the merchant selects B (buying the goods) because it has the greater present value (or, what amounts to the same thing, because the rate, 10 per cent., of the return of $1100 on the sacrifice of $1000 is greater than the rate of interest, 5 per cent.); then he selects C (borrowing money), which has the same present value as B, but a more desirable time-shape. This description takes account of the whole series of operations, and corresponds to the principles propounded in Chapter VIII. 3. It is the third option A which gives rise to the con-

tention that the loan produces a profit not possible or easy without it, and that it is, therefore, ‘“‘productive.’’ We have just seen that the loan phenomena are resolved into two separate steps, the rejection of A in favor of B, and the rejection of Bin favor of C. Yet since it may often happen, as shown in Chapter VIII, that the first step (choice of options) would not be taken unless the second step (loan)

were already in contemplation, it is true that, in a sense,

Sxc. 7]

APPLICATION

TO ACTUAL

CONDITIONS

251

the choice of the loan includes the choice between the options A and B. Looked at in this way, the effect of the loan is measurable by comparing CG with A, such comparison including both the steps stated. In this sense, and in this sense alone, is the loan “productive.” It is productive in that it enables the merchant to buy the goods. He thus chooses an option (B) which has an advantage (over A) in present value, or yields a rate of return on sacrifice (10 per cent.) greater than the rate of interest. The reason that the loan is regarded as “productive,” then, is that it gives the merchant the opportunity to make 10 per cent. instead of 5 per cent. But obviously it is not the loan (choice of C rather than B) which yields the 10 per cent., but the choice of options without the loan (B rather than A). The profit is the advantage of B over A; but the loan merely substitutes C as a more desirable equivalent of B. It does not add to the profit, though it changes the form in which it appears. After the loan, the profit appears in the accounts for 1902 in the form of $50 more income for C than for A. If, after all has been said and understood, any one still prefers to call such a loan “productive,” no objection is offered, provided always that it is made wholly clear

what is meant by the term “ productive.” The essential point is that our theory of interest is not restricted in its application to personal and public loans, but includes the loans of business. These business loans come into the same theory as the other loans, and differ only in the existence of a wider range of choice in incomestreams.

§7 We have seen that the theory of interest which has been propounded is adequate to explain the motives which lead

to borrowing and lending in the actual business world. The purpose of loans in all cases may be said to be to modify

the shape of income-streams so as to suit the particular

252

THE

RATE

OF

INTEREST

[CHar. XIII

requirements of the case, — to increase present income at the sacrifice of future, and to eke out present scarcity As Jevons stated, in anticipation of future abundance. capital is required to enable one to support himself while engaged in undertakings which require time. The foregoing classification is made from the standpoint of the borrower. From the standpoint of the lender, loans do not need to be so minutely classified. The lender is usually either one who wishes to invest permanently, or one who wishes to invest temporarily. The former may lend on mortgage, or he may buy the securities of companies, governments, or municipalities, or he may be a depositor in a savings bank. In all cases the lender is evidently sacrificing what he might enjoy in present income, in order that he may have a still larger income in the future. In other words, he is modifying the time-shape of his income curve in a manner opposite to that which the borrower pursues. When he invests for short times, this course is generally due to a periodic fluctuation in his income-stream, the large present flow being precedent to a shortage in the not far distant future. Business men and institutions are in this way

constantly investing for short periods funds which otherwise would exist in the form of idle cash. The government or individual which we supposed to have borrowed at the time of deficit in anticipation of surplus may, instead, follow the reverse policy of investing the surplus at interest, in order to provide better for the payment of expenses at the time of anticipated deficit.

§ 8 The same person may be alternately borrower and lender,

according to the exigencies of his income-stream.

When the

same person is simultaneously borrower and lender, he be-

comes a broker for managing credit operations for other persons. This is usually the function of institutions such as banks of discount and deposit, savings banks, trust companies, exchange brokerage firms, and mortgage companies.

Sec. 8]

APPLICATION

TO

ACTUAL

CONDITIONS

253

It is through such firms that borrowers and lenders usually reach each other, rather than directly ;but whether directly or by means of such intermediaries, the borrowers and lenders are constantly playing into each other’s hands.

This is particularly evident in the case of periodic fluctuations; for it usually happens that the same cycle of operations which makes one man’s income alternately large and small will make another man’s alternately small and large. Thus, when the clothing manufacturer sells to the retailer of ready-made clothing, not only does this operation tend to make inroads in the income-stream of the latter, but it also tends to bring to the former an accession of income inconveniently concentrated. For this reason the manufacturer may decide to keep the commercial note which the clothier makes to him, rather than to discount it at a bank. The manner in which fluctuations in income-streams mutually compensate among borrowers and lenders is well seen in the South, where cotton planters have long been accustomed to borrow of the banks in springtime, to repay in the fall after the cotton is sold. Until recently the banks

which supplied these loans found difficulty in leveling the consequent irregularities produced in their own incomestreams. They were forced to do so largely by keeping an idle stock of cash, or investing it at low rates in Northern banks. But recently cotton mills have settled in the South, with a cycle of income exactly the reverse of that of the planters. They buy their crops in the fall, manufacture through the winter, and sell in the spring. The consequence is that they come to the banks for loans in the fall, which is just the time when the banks are receiving their pay from the planters, and liquidate these loans in the spring, at just the time when the banks are in need of funds to lend to the planters. In this way the irregularities in the income-streams of both planters and manufacturers are leveled, virtually by mutual cancellation, but actually through the intermediation of the banks.

254

THE

RATE

OF INTEREST

(Cuap, XIII

§ 9 Hitherto we have considered loans only with reference to the time of issue and repayment. But it frequently happens that loans are transferred at points intermediate between these two dates. In that case they pass by sale like other property, and affect the income-streams of those who buy and sell in precisely the same way as if they lent and borrowed. The buyer of a security is in the same position as a lender,

—he parts with present income for the sake of future. The seller of a loan security is in the same position as a borrower, —he is securing present income and foregoing the future interest he would otherwise receive. The price at which such loan securities are sold will determine the rate of interest realized and borne by the buyer and seller respectively. The effects caused by the transfer of loans may be negatived by later transactions. The seller of a bond may not really use the proceeds to swell a large income, but may reinvest in some other security, and the buyer may not hold the security until maturity, but may sell again at the next turn of the market. What has been said of loan securities applies also to every form of property which may be regarded in the same light. The buyer of railway stock is not very different from the buyer of railway bonds, or the lender. He also is sacrificing present income for future, so far as this particular purchase is concerned, even though, as just shown, the effect may be negatived by some other transaction. Likewise the seller of railroad stock is similar to the seller of bonds, or the borrower. The only distinction is that in the case of buying and selling stock the rate of interest is implicit rather than explicit. § 10

Explicit and implicit interest really differ, however, in degree rather than in kind. An income bond, while

Suzc.10]

APPLICATION

TO

ACTUAL

CONDITIONS

255

nominally yielding explicit interest, may actually, if the

income is inadequate, yield quite a different interest, and the price of sale takes into account the latter contingency quite as much as the former. Preferred stock, likewise, while nominally involving the risk of non-payment, often represents a case more nearly like that of explicit interest. It is quite as possible, on the basis of the purchase price and the practical certainty of a definite fixed income, to calculate the rate of interest to be realized to the investor, as in the case of the bond buyer. In the case of ordinary stock, however, in order to calculate the interest to be realized, it becomes necessary to make a forecast of the probable dividends. It is where the element of chance thus enters that implicit interest really differs from explicit.

Where the ownership of an article of wealth is total instead of partial, the element of chance is always present. In fact, bonds, so far as they escape from the universal reign of chance, do so only by carving out of the fluctuating income

arising from a mass of capital-wealth a certain definite part, small enough not to absorb the whole even at its lowest ebb. But while the rate of interest is somewhat difficult to calculate in advance in the case of other property than loan securities, it may be approximately estimated, and from the rate which has been actually realized in the past it may sometimes even be exactly calculated. In the case of land, it is not uncommon to reckon the value of so many years’ purchase of the crop returns, on the assumption that the same value of the crop returns will continue indefinitely. The element of risk, which is so dominant in actual business relations, has also been considered in the theory of this book. The buying and selling of property serve to modify not only the time-shape of the income-stream, but also the degree of certainty. The investor who wishes to take chances may invest in stock, and he who does not, in bonds. Risk constitutes the real difference between them, and the reason for the existence of the two types of securities. Both are investors, and both sacrifice present

256

THE

RATE

OF

INTEREST

[Coav. XIII

income for future; but one assumes a future income with risk and the other receives one without risk, or at any rate, with no large degree of risk. That stockholders and bondholders are both investors is not inconsistent with the fact already emphasized that the stockholder is a borrower of the bondholder as a lender. In dealing with each other they are on opposite sides of the market, the bondholder being a buyer or investor and the stockholder a seller or borrower. But in dealing with ‘the company,” they are on the same side of the market ; both are buyers of securities, or investors. Thus by borrowing and lending, or by buying and selling, an individual regulates the character of his income-stream to suit his individual needs and idiosyncrasies. This adjustment involves comparisons of risk and of futurity, and in the latter case involves a rate of interest, implicit or explicit. This rate is utilized by individuals to enable them to increase or decrease the flow of their income at

different periods of time, and it is through their efforts to do so, by bargaining with each other, that the rate of interest is itself determined. The theory of its determina-

tion applies to the actual loans of business, loans of necessity, improvidence, or purchase, loans of persons, corporations, and loan brokers, and applies also to cases in which there are no contract loans at all, but only the buying,

selling, and valuing of property, in which transactions the rate of interest is always implicitly contained.

CHAPTER INDUCTIVE

XIV

VERIFICATION

(MONETARY)

§ 1

No study of the principles governing the rate of interest would be complete without verification by facts. In this chapter those facts will be presented which bear on the problem discussed in Chapter V, the problem of appreciation and interest. The object will be to ascertain the extent to which, in the actual world, the appreciation or depreciation of the monetary standard is foreseen by borrowers and lenders, and provided for in the rates of interest upon which they agree. At the outset the question arises, How can a merchant be said to foresee the appreciation of money? Appreciation is a subtle concept. Few business men have any clear ideas about it. Economists disagree as to its definition, and statisticians as to its measurement. If we ask a merchant whether or not he takes account of appreciation, he will say that he never thinks of it, that he always “regards a dollar as a dollar.” In his mind, other things may change in terms of money, but money itself does not change. Yet it may be true that he does take account of a change in the purchasing power of money, under guise of a change in the prices of other things. In our daily life we seldom think of the earth as moving; nevertheless we take account of its rotation whenever we speak of “sunrise” or “sunset.” During a period of paper-money inflation the ordinary man

conceives the premium on gold as a rise of gold bullion, not a fall of the paper money; but he arrives at the same practical results. Appreciation of money, whether in reference to gold bullion, commodities, or labor, is in effect taken account of in the practical man’s forecast of 8

257

258

THE

RATE

OF INTEREST

[Cuar. XIV

all the economic elements which concern him, — the prices of his product, the cost of his living, the wages of his workmen,

and so forth.

Moreover,

he takes account

of the

relative importance of these factors as affecting himself, and not of their relative importance in the elaborate averages of the statistician, — averages which may emphasize some particular commodity or labor whose fluctuations have no interest for him. His own aim is not to predict the index numbers of Sauerbeck or of the United States Bureau of Labor, but to foresee those price changes which affect his own economic future. To foresee a rise or fall of a particular price is to that extent to foresee a change in the purchasing power of money. Such forecasts enable a man to make reasonably correct decisions, and in particular to contract a loan with intelligence. If gold appreciates in such a way or in such a sense that he expects for himself a shrinking margin of profit, he will be cautious about borrowing unless interest falls; and this very unwillingness to borrow, lessening the demand in the “money market,” will bring interest down. On the other hand, if inflation is going on, he will see rising prices and rising profits, and will be stimulated to borrow capital unless interest rises; moreover, this willingness to borrow will itself raise interest. Foresight is clearer and more prevalent to-day than ever before. Multitudes of trade journals and investors’ reviews have their chief reason for existence in supplying data on which to base prediction. Every chance for gain is eagerly watched for. An active and keen speculation is constantly going on which, so far as it does not consist of fictitious and gambling transactions, performs a wellknown and provident function for society. Is it reasonable to believe that foresight, which is the general rule, has an exception as applied to falling or rising prices?

§ 2

Appreciation and depreciation in this book are used in a purely relative sense. If gold appreciates relatively to

Sec. 2]

INDUCTIVE

VERIFICATION

(MONETARY)

259

silver, then necessarily silver depreciates relatively to gold. Any standard appreciates 1 per cent. relatively to another standard if a certain amount of it now commands 101 units in this other standard, when previously it commanded only 100 units. General evidence that an expected appreciation or depreciation of money has an effect on the rate of interest in

that money can be obtained from several sources. During the free-silver agitation of 1895-6, it was observed that municipalities could often sell gold bonds at better terms than “currency” or “coin” bonds. There was a strong desire on the part of lenders to insert a gold clause in their contracts, and they were willing to yield something in their interest to secure it. The same tendency was

strikingly shown in California‘ during the inflation period of the Civil War. For a time, gold contracts could not be enforced, and in consequence

interest rates were excep-

tionally high. During a period of progressive paper inflation the rate of interest in contracts drawn on a paper basis is high. This was true during the Civil War, and also during the currency troubles in the thirties. Raguet wrote:? “In the six months before the suspension of ’37, although the amount of the currency was greater than it had ever been before in the United States, yet the scarcity of money was so great that it commanded from 1 per cent. to 3 per cent. per month.”’ It would be unsafe to found much inference on these facts; their significance may be partly or wholly

different. But they raise a presumption that anticipation of further depreciation of currency tends to increase the rate of interest. A definite test must be sought where two standards are

simultaneously used.

An excellent case of this kind is

1 Bernard Moses, “Legal Tender Notes in California,” Quarterly Journal of Economics, October, 1892, p. 15. 2 Currency and Banking (1839), p. 139; also Sumner, History of Banking, New York (1896), p. 264.

THE

260

RATE

(Cuar. XIV

OF INTEREST

supplied by two kinds of United States bonds, one payable in coin and the other in currency. From the prices which these bonds have fetched in the market it is possible to calculate the interest realized to the investor. The cur-

rency bonds were known as currency sixes and matured in 1898 and 1899. The coin bonds selected for comparison were the fours of 1907. The following table gives the rates

of interest realized in the two standards, together with the premium on gold. RATES

Jan., July, Jan., July, Jan., July, Jan., July, Jan., July, Jan., July, Jan., July, Jan., July, Jan., July,

OF

1870 1870 1871 1871 1872 1872 1873 1873 1874 1874 1875 1875 1876 1876 1877 1877 1878 1878

INTEREST REALIZED FROM DATES TIONED TO MATURITY '* Corn

ae

Pricn or Gop

| 6.4 | 5.8 | 6.0 | 5.8 | 5.3 | 5.6 | 5.7 | 5.4 | 5.0 | 5.1 | 5.0 | 5.1 | 4.7 | | 4.5 | 4.5 | 4.4 | 5.0 | 3.9

5.4 5.1 5.3 5.0 4.9 5.0 5.1 5.0 5.0 4.9 4.7 4.4 4.4 4.2 4.4 4.3 4.6 4.4

119.9 112.2 110.8 113.2 109.5 113.9 111.9 115.3 110.3 110.7 112.6 117.0 112.9 112.3 107.0 105.4 102.8 100.7

MEN-

Corn bade

Jan., Jan., Jan., Jan., Jan., Jan., May, Jan., Jan., Mar., Jan., May, July, Jan., Mar., Nov., Aug., Aug.,

1879 1880 1881 1882 1883 1884 1885 1886 1887 1888 1889 1890 1891 1892 1893 1894 1895 1896

1 This table has been obtained by the aid of the bond tables. In the case of currency bonds, it was to deduct accrued interest (if any) from the quoted in the table for the interest which corresponds to the and the number of years to maturity. In the case

| 3.7 | 3.8 | 3.3 | 3.0 | 2.9 | 2.6 | 2.7 | 2.6 | 2.3 | 2.3 | 2.2 | 2.1 | 2.4 | 2.6 | 2.8 | 2.7 | 2.8 | 3.2

| 4.5 | 4.0 | 3.4 | 3.5 | 3.3 | 2.9 | 2.7 | 2.6 | 2.6 | 2.9 | 2.6 | 2.6 | 3.0 | 3.1 | 3.1 | 3.5 | 3.6 | 4.3

usual brokers’ only necessary price and look price so found of coin bonds,

Sec. 3]

INDUCTIVE

VERIFICATION

(MONETARY)

261

Several points in this table deserve notice. In 1870 the investor made 6.4 per cent. in gold but was willing to accept a return of only 5.4 per cent. in currency.

This fact

becomes intelligible in the light of the theory which has been explained. It meant the hope of resumption. Because paper was so depreciated there was a prospect of a great rise in its value. It was not until 1878, when the prospect of a further rise disappeared, that the relative position of the two rates of interest was reversed. After resumption in 1879 the two remained very nearly equal for several years, until fears of inflation again produced a divergence. The quotations for 1894, 1895, and 1896 show a considerably higher rate of interest in the currency standard than in the coin standard, as well as a higher rate in both standards than in previous years. The difference is between 2.7

per cent. and 3.5 per cent. in 1894, and between 3.2 per cent, and 4.3 per cent. in 1896. Both the increase and the wedging apart of the two rates are explainable as effects of the free-silver proposal and its incorporation (July, 1896) in the platform of the Democratic party.

§ 3 We see, therefore, that the facts agree with the theory previously laid down. But it is necessary further to inquire how close is this agreement. For this purpose the figures just given are of little value. They represent the rates of interest realized for the periods between the dates named and the times at which the bonds matured;

but as these

since the quotations are given in currency, it is necessary to divide the quoted price by the price of gold in order to obtain their price The in gold (i.e. coin”), and then proceed as above indicated.

quotations of prices of bonds and gold are the ‘‘opening”’ prices for the months named, and are taken from the Financial Review (Annual Summary of the Commercial and Financial Chronicle), 1895, The Commercial and Financial Chronicle, the (New York) Bankers’ MagaAfter 1884, January quotations zine, and the Bankers’ Almanac. were not always available.

262

THE

RATE

INTEREST

OF

[Cuap. XIV

periods are not the same for the two bonds, the two corresponding series of interest rates are not entirely comparable. Such a rate of interest is a sort of average of the rates of interest for the individual years of the periods in question.! Thus, in the foregoing table, the rate of interest in currency placed opposite January, 1870, is 5.4 per cent. This is the rate realized between 1870 and 1899. It is a sort of average of, say, the rate of interest for the period RATES OF INTEREST REALIZED FROM DATES MENTIONED TO JANUARY 1, 1879 (DATE OF RESUMPTION) ? APPRECIATION OF CURRENCY IN GOLD

CoIn

CuRRENCY

‘“ Expected ”

Jan., 1870 . . July, 1870 . . Jan. e187 ie ve July aS 7 Jan. p13 02a July, 1872 =: Jan. 1873. July yslSiomemee Jan., 1874 . . July, 1874. . Jan., 1875 . . July, 1875 . . VAN. ES¢O) erm July, 1876 . . APNG aNCVI(e 5 Jnly; 18i7- "| ae: Jan., 1878 . . July, 1878 . .

4)

4

tall 6.2 6.7 6.4 5.9 6.2 6.5 6.2 5.6 5.7 6.0 6.1 5.4 5.2 5.5 5.7 8.2 4.8

6.3 5.7 6.3 5.7 5.7 5.7 6.2 6.0 6.1 5.8 5.4 4.2 4.1 2.4 4.0 3.1 6.0 2.6

Actual

a

8 5 4 7 2 5 3 Zz —.5 = 1 6 1.9 1.3 2.8 1.5 2.6 PAP 2.2

2.1 1.4 13 1.8 1.3 2.1 2.0 2.8 2.1 2.4 3.1 4.9 4.3 4.9 3.5 3.6 2.8 1.4

1 For the nature of this average, see The Nature of Capital and Income, Appendix to Chap. XII, § 5. ? Since the figures in this table represent the rates of interest which will render the “present value,” at the date of purchase, of all the future benefits up to January, 1879, equal to the purchase price, they can be calculated by Horner’s method as indicated in § 9

Szc. 3]

INDUCTIVE

VERIFICATION

(MONETARY)

263

between 1870 and 1879 (which, as we shall see, was 6.3 per cent.) and that for the period between 1879 and 1899

(which was 4.5 percent.).

For a true comparison between

coin and currency rates, we must seek rates relating to the same period in each case. This is the method in the fol-

lowing table.

In it, the periods selected all terminate on

January 1, 1879, the date of resumption of specie payments. The rates of interest in this table are the rates which would be realized by investors who should buy the bonds at the dates mentioned and sell them on January 1, 1879. of the Appendix to Chap. V. But the method which has been adopted is less laborious, as it enables us to use the bond tables. It can best be explained by an example. The opening price, January, 1870, of currency sixes was 1094, and in January, 1879,the price was 119}. These prices require no correction for accrued interest. Our problem is, if a man spends $109} in 1870 and receives $1193 in 1879 with $6 per annum (semiannually) in the meantime, what rate of interest does he realize? Now it is clear that the answer is the same if all the benefits and sacrifices involved are doubled or halved or increased or decreased in any common ratio. Let us then divide them all by 1.194. Then we would have $91.3 paid in 1870 for $100 due in 1879, and $5.02 per annum in the meantime. That is, the rate of interest realized is exactly as if the bond were a 5.02 per cent. bond maturing in 1879 and bought at 91.3in 1870. This rate can readily be obtained from the bond tables by interpolating between the figures for a 5 per cent. and a 54 per cent. bond purchased at 91.3 with 9 years to run. For a 5 per cent. bond we obtain 6.28 per cent. and for a 53 per cent. bond, 6.81 per cent. Hence for a 5.02 per cent. bond the result is 6.30 per cent. The third column gives what may be called the expected rate of appreciation of currency in terms of gold; that is, that rate of appreciation which would have made the two interest rates equally profitable. It is therefore the difference between the two rates of interest. Finally, the last column gives the actual rate of appreciation between the dates mentioned and January 1, 1879. This is calculated from the quoted prices of gold. Thus the opening price of gold January, 1870, was 119.9, and January, 1879, 100. Hence currency appreciated in nine years in the ratio of 100 to 119.9, which is at the rate of 2.1 per cent. per annum. If the appreciation proceeded uniformly, this method would be strictly correct. As it is, a more elaborate method would be required, in accordance with the principles explained in § 9 of the Appendix to Chap. V, to take account But for our fully of the fluctuations of the annual appreciation. present purposes, and for results worked out to but one decimal place, the simpler method here adopted is sufficiently correct.

264

THE

RATE

OF

INTEREST

[Caap. XIV

From this table we see that the rates of interest realized for the period, January, 1870 to January, 1879, were in coin, 7.1 per cent., and in currency, 6.3 per cent., the difference ! between which is .8 per cent., the rate of appreciation which would equalize the investments in the two bonds.

This may

be called the “expected appreciation.”

The

actual rate of appreciation was 2.1 per cent. That is, the estimated appreciation was about two-fifths of the appreciation as it really turned out. Those who held currency

sixes therefore had the better investment

during 1870-

1879. In fact, it is well known that many speculators grew rich by exchanging gold bonds for currency bonds about this time. The table shows that there was the same underestimate of future appreciation in July, 1870, January, 1871, and July, 1871. From that time to July, 1874, the table shows that the outlook for resumption grew gloomy, due no doubt to the strong greenback sentiment. The inflation bill of 1874 actually produced a prospect of negative appreciation; 7.e. depreciation. This bill was vetoed by President Grant, and in December

of that year the bill for resumption was passed by the Senate. Accordingly, January, 1875, opened with a more hopeful estimate. The bill became a law on the 14th of January, and there was an immediate rise in the “expected appreciation” which from that time forward averaged

2 per cent.

But during the same period the actual ap-

1 The formula used is therefore simply

7

=i+ a.

(7 represents the

rate of interest in coin, 7 the rate of interest in currency, a the expected

rate of appreciation—that is, the rate of appreciation of the currency standard with respect to the coin standard). As shown in Appendix to Chap. V, § 3, this formula applies strictly only when the rates of interest and of appreciation are ‘“‘reckoned continuously.’ But practically it applies to all cases with which we have to deal, as the interest periods are seldom over half a year. Even when the interest is payable only annually, and, in consequence, the correct formula is 1 + 7 = (1+ 7%) (1+), (see Appendix to Chap. V, § 2), the value of a calculated by this formula will seldom differ perceptibly from its value calculated by the simpler formula 7 =7+ a, here employed.

Szc.4]

INDUCTIVE

VERIFICATION

(MONETARY)

265

preciation from the dates named to January, 1879, averaged 3.6. per cent., so that even after the government promised resumption, investors and speculators did not put implicit confidence in that promise, the “expected appreciation” being only a little more than half the actual appreciation. This corresponds to the well-known fact that the resumption act was looked upon as a political maneuver, likely to be repealed.! § 4

Having compared the rates of interest in paper and coin, we may next compare them in gold and silver. The comparison, to be of value, must be between gold and silver contracts in the same market and with the same security. Such contracts are fortunately available in the London market of government securities. The loans of India 1 It should be observed that the method employed to determine the rate of interest realized is open to one danger. It correctly represents the rate of interest actually realized between two dates, but, unless the later of the two dates is maturity, it does not necessarily represent the rate of interest expected at the first date. The investor could not know in January, 1870, what the price of bonds would be in January, 1879, unless the bonds matured at that time. To accurately compare, in 1870, the relative advantages of coin and currency bonds for the period 1870-1879, a forecast would have been necessary,

not only of the relation of currency to gold, but also of the prices of the two bonds in 1879. These prices, in turn, depend on a new forecast made in 1879. It follows that a mistake in this forecast of 1879 and embodied in the prices of that year would affect the rate of interest realized between 1870 and 1879 in the same manner as a mistake of the opposite kind in the forecast of 1870. But in most cases the method given is sufficiently exact. For, although in 1870 it would have been impossible to predict exactly the prices of the two bonds in 1879, yet it can usually be depended upon that any great change in price is apt to affect both alike, and thus eliminates itself for the most part in the comparison. The reason that the errors in predicting what the prices of the two bonds would be in 1879 are nearly equal is that the two bonds selected were ap-

proximately of the same term. The coin bonds matured in 1907, the currency bonds in 1898 and 1899. The eight or nine years beIt is for this reason tween them would be almost immaterial in 1879. that the coin bonds of 1907 were chosen in preference to those of 1881.

RATE

THE

266

OF

INTEREST

[Cuar. XIV

have been made partly in gold and partly in silver, and both forms of securities are bought and sold in London.* The interest on the silver, or rather rupee, bonds is paid by draft on India. The sums actually received in English money depend on the state of the exchanges. The rate of interest in the silver standard is calculated in the same way as was shown? for coin bonds in § 3. The results are contained in the following table :— RATES

OF INTEREST REALIZED FROM DATES TO MATURITY OR IN PERPETUITY?

DIFFER-

NAMED

EXCHANGE

ia

eae

ENCE

1865 1868

4.3 4.3

4.1 4.0

2 3

23.2 23.0

1870 1871 1872 1873 1874

4.3 4.1 3.9 3.9 3.9

4.0 3.8 3.7 Sea 3.8

3 3 2 2 el

23.6 23.2 22.6 22.4 22.2

ON

|PEncE ae

1 The silver bonds or ‘‘rupee paper” were issued to raise loans in India, but they have also been enfaced for payment in England, and in 1893-1894 some Rs. 25,000,000 were on the London books. — Burdett’s Official Intelligencer (1894), p. 75. ? Thus in 1880 the average price paid in London for ‘‘rupee paper’”’ of face value Rs. 1,000 yielding 4 per cent., or Rs. 40 per annum, was £79. In order to find the rate of interest realized by the investor, we must translate £79 into silver. The average rate of exchange in 1880 was 20d. per rupee. Hence £79 were equivalent to 948 rupees. That is, speaking in terms of silver (or, more exactly, in terms of exchange on India), the price of a 4 per cent. bond was 94.8, which, if the bond be treated as a perpetual annuity, yields the investor 4.3 per cent. In the same year, an India gold bond yielded 3.6 per cent. 5 This table is formed from averages of (usually ten) quotations distributed through each year, taken from the Economist, the Investor’s Monthly Manual, and the (London) Bankers’ Magazine. The fourth column is founded on the table in the Report of the Indian Currency Committee (1893), p. 27, but is corrected to apply to calendar instead of official years.

Src. 4]

INDUCTIVE

VERIFICATION

(MONETARY)

267

RATES OF INTEREST REALIZED FROM DATES NAMED TO MATURITY OR IN PERPETUITY —Continued

Goip?

DIFFER-

ENCE

EXCHANGE

InDIA

PENCE

1875 1876 1877 1878 1879 1880 1881 1882 1883 1884 1885 1886 1887 1888 1889 1890, Ist half 1890, 2d half 1891 1892 1893 1894

3.6 a7 3.7 3.9 3.7 3.6 3.4 3.5 3.4 3.3 3.5 3.5 3.4 34 3.0 3.0 a4 3.1 3.1 3.0 3.0

4 4 4 3 rs 7 6 A 7 8 6 6 7 1.0 Pst 1.0 8 4 8 9 9

ON

PER RUPEE

21.9 20.5 20.9 20.2 19.7 20.0 19.9 19.5 19.5 19.5 18.5 17.5 17.2 16.5 16.5 17.6 19.3 171 15.3 15.0 13.5

1 The quotation from which the interest was computed for 1895 and succeeding years is for 34 per cent. rupee paper. All previous quotations are for 4 per cent.’s. The 4 percent.’s were repayable on three months’ notice; this notice was given in 1894, and the bonds redeemed or converted into 34 per cent.’s before the close of the year. To obtain the rate of interest realized, the London quotations in pounds sterling are first converted into rupees at the current rates of exchange, and then the bonds are treated as perpetual annuities. The results differ from those given in the Investor’s Monthly Manual, because the rupee is there converted at a conventional value, not the market value. ; 2 From 1865 to 1880 inclusive the figures refer to 4 per cent.’s, repayable October, 1888, or later; those of 1881-1884 are for 34 per cent.’s maturing in 1931, and those for 1885-1906 are for 3 per cent.’s maturing in 1948.

268

THE

RATE

OF

[Cuar. XIV

INTEREST

RATES OF INTEREST REALIZED FROM DATES NAMED TO MATURITY OR IN PERPETU Concluded — ITY

RuPEE

Gop

Diese ENCE

ot Pence

ata PER

1895

3.4

2.8

6

13.4

1896

3.0

3.1

wy:

14.3

1897

3.5

oe

A

ieoek

1898

aon

oe

as

16.0

1899

3.6

3.2

A

16.1

1900

Dial

3.4

3

16.0

1901

Sill

3.5

2

16.0

1902

3.6

3.5

1

16.0

1903

3.0

3.5

0

16.0

1904

3.6

3.7

—.l

16.1

1905

3:6

3.6

0

16.1

1906

3.6

Be

4

16.0

wri RUPEE

From this table it will be seen that the rates realized to investors in bonds of the two standards differed but slightly until 1875, when the fall of Indian exchange began. The average difference previously to 1875 was .2 per cent., while the average difference from 1875 to 1892 inclusive was .7 per cent., or more than three times as much. Within this period, from 1884 exchange fell much more rapidly than before, and the difference in the two rates of interest rose accordingly, amounting in one year to 1.1 per cent. Inasmuch as the two bonds were issued by the same government, possess the same degree of security, are quoted side by side in the same market, and are similar in all other respects except in the standard in which they are expressed, the results afford substantial proof that the fall of exchange (after it once began) was discounted in advance and affected the rates of interest in those standards. Of course

investors did not form perfectly definite estimates of the future fall, but the fear of a fall predominated in varying degrees over the hope of a rise.

Szc. 4]

INDUCTIVE

VERIFICATION

(MONETARY)

269

The year 1890 was one of great disturbance in exchanges, the average for the first six months being 17.6 and for the last six months 19.3. The gold price of the silver bonds rose from an average for the first six months of 73.8 to 83.5 for the last six months, but the rise in their silver price was only from 100.6 to 103.7, showing that the increase of confidence in the “future of silver” was not great, and in fact only reduced the disparity in the interest from 1.0 to .8 per cent. This great rise in exchange and the slight revival in silver

securities occurred simultaneously with the passage of the Sherman Act of July, 1890, by which the United States was to purchase four and a half million ounces of silver per month. There can be little doubt that the disturbance was due in some measure to the operation or expected operation of that law. This is not the only case in which the relative prices of rupee paper and gold bonds were probably affected by political action. One of the smallest differences in the two rates occurs in 1878, which was the year of the Bland Act and the first international monetary conference. After the closure of the Indian mints on June 26, 1893, exchange rose from 14.7 to 15.9, the gold price of rupee paper from 62 to 70, and consequently its rupee price from 101.2 to 105.7. From this point the exchange again dropped, much to the mystification of those who had predicted an established parity between gold and silver at the new legal rate of 16d. per rupee. There was much discussion as to the reasons for the failure of the legal rate to become operative. The reason seems to have been that the closure of the mints to silver attracted into the circulation silver from other channels, especially old Native hoards. Within a few years, however, this source of supply

was dried has been variations But until

up so that the legal par was reached in 1898 and maintained ever since, subject only to the slight of exchange due to the cost of shipping specie. the par was proved actually stable by two or

270

THE

RATE

OF

INTEREST

[CHar. XIV

three years’ experience, the public refused to have confidence that gold and the rupee were once more to run

parallel.

Their lack of confidence was shown in the dif-

ference in the rates of interest in gold and rupee securities during the transition period, 1893-1898, and the two or three succeeding years. From 1893 to 1900 inclusive the two rates averaged .5 per cent. apart. From 1901 to 1906 inclusive, the average difference was only .1 per cent.’

§ 5 We shall next attempt to apply the theory of appreciation and interest to periods of rising and falling prices. We are met, however, by the difficulty that comparison can only be made between successive periods. We can learn what the rate of interest has been during a price movement, but we cannot know what it would have been if that price movement had not taken place. Without this missing term of comparison, it is difficult to measure the influence of the rise or fall in price level. No two periods are so alike industrially that we can say they differ only in the state of the monetary standard. Other influences innumerable affect the ‘value of money.” In spite of these difficulties, however, certain general conclusions can be established. It must be borne in mind that we are studying the effects of rising, not high, prices, and of falling, not low, prices.

Falling prices are as different from low prices as a waterfall is from sea level. Our study is not of price levels, but of the slopes between price levels.” 1 The preceding comparisons serve only to establish the influence of the divergence between the standards on the rates of interest, but afford no measure of that influence. In order to measure the extent to which the fall of silver was allowed for by investors, it would be necessary to examine the rates realized during specific periods, as in the case of coin and currency bonds considered in § 3. A somewhat unsatisfactory attempt to do this was made in “ Appreciation and Interest,’”’ but is not reproduced here. The case is unlike that of the United States coin and currency bonds, since in the case now under discussion, the two kinds of bonds, rupee and gold, did not have approximately the same date of maturity. > De Haas appears to have fallen into the confusion between high

Sec.5]

INDUCTIVE

VERIFICATION

(MONETARY)

271

It was once predicted by Mr. H. H. Gibbs, formerly a director of the Bank of England, that the progressive scarcity of gold would raise the rate of interest. He reasoned that such scarcity would make a stringency in the money market, and that the banks, each struggling to attract reserves from the others, would raise their rates. This prophecy, however, was not fulfilled. The theory that appreciation raises interest has been frequently affirmed, and has even received the stamp of approval of Mr. Robert Giffen. But it is utterly at variance with facts. When prices are rising or falling, money is depreciating or appreciating relatively to commodities. Our theory would therefore require high or low interest according as prices are rising or falling, provided we assume that the rate of interest in the commodity standard does not vary. This assumption would be thoroughly justified only in case the

two periods were alike in all respects except in the expansion or contraction of credit and currency. In the following table for London the periods are selected to correspond with the main movements of prices. Thus, the period 1826-1829 was a period of falling prices, so that money appreciated in terms of commodities at the average

rate of 4.2 per cent. per annum. This is indicated in the third column by the figure + 4.2. In the period 1836-1839 prices rose so that money fell at the rate of 2.3 per cent. per annum, indicated by —2.3. The fourth and last column indicates the rate of interest which is virtually paid in commodities. It is the rate of commodity-interest equivalent to the market rate of money-interest actually paid, and therefore is, in each case, the sum of the two items of the two preceding columns. and rising prices, both in his criticism of Jevons and in his treatment See ‘‘A Third Element in the Rate of Interest,” Jourof statistics. nal of the Royal Statistical Society, March, 1889. 1 The Bimetallic Controversy, London (Wilson), 1886, pp. 19, 231 245-249, 373.

2 See “Appreciation and Interest,’

p. 57.

THE

272

LONDON

OF

RATE

INTEREST

RATES OF INTEREST IN RELATION AND FALLING PRICES’

[Cuar. XIV

TO RISING ST

a eee

MARKET

a 1826-1829 1830-1835 1836-1839 1840-1844 1845-1847 1848-1852 1853-1857 1858-1864 1865-1870 1871-1873 1874-1879 1880-1887 1888-1890 1891-1896 1897-1900

1901-1906

4.4 4.0 4.7 4,2 Sei 2.9 4.1 4.4 3.8 3.9 3.2 3.3 3.8 2.5 3.2 3.6

3.5 3.2 4.2 3.5 4.2 2.5 5.3 4.2 3.6 3.7 20. 2.6 2.9 1.5 2.6 3.1

VIRTUAL APPRECIATION INTEREST IN or MoneEy IN | COMMODITIES

CoMMODITIES

(Market)

a

]

+ 4.2 0.0 — 2.3 + 5.9 — 3.0 cd 1.2 — 2.4 = 1.0 + 1.1 O28 + 4.3 + 3.8 —14 + 3.4 — 6.6 1.5

ioe 3.2 1.9 9.4 1.2 ost 2.9 1.2 4.7 — 2.5 7.0 6.4 1.5 4.9 — 4.0 1.6

1This table is constructed from the data given in the Appendix to this chapter. The third column is based on index numbers (Jevons’ for 1826-1852, and Sauerbeck’s for the remaining years). The index numbers for two dates, as 1826 and 1829, being given, their, inverse ratio gives the relative value of money (in commodities) at those two dates. From these it is easy to calculate the average annual change in its value. The method is the same as that employed for finding the rate of interest by which $1, by compounding, will amount to a given sum in a given time. Theoretically, since the loans here included run usually perhaps thirty to ninety days, the quotations of rates of interest averaged should begin at the first of the two dates, and cease, say, sixty days before the second. But the index numbers are not always for definite points of time, nor can the interest quotations be subjected to such minute corrections without an immense expenditure of labor. Hence, the method adopted has been to average the rates for all the years of a period; e.g. for the four years, 1826-1829. The “appreciation” is reckoned between those dates. If the index numbers represent the price levels at the middle of 1826 and 1829, then the average interest rates ought in theory to include only the last six months of 1826, and the first four months of 1829. But it seems better to include too much at both ends than to omit the averages for 1826 and 1829 altogether, for the reason that an average is the more valuable the greater the number of terms included.

Sec.6]

INDUCTIVE

VERIFICATION

(MONETARY)

273

If this table be examined, it will be found that if, in comparing one period with the next, the rate of interest falls, the “appreciation ”’ usually rises, or if the rate rises, the “appreciation” falls. The comparison of each period with the one following may be designated as a “se quence.” In twelve out of fifteen sequences for bank rates and in eleven out of fifteen for market rates, interest

is high or low according to the rising or falling. Attention is period 1853-1857, during which taneously with, and presumably production. The market rate per cent., which was far higher,

degree in which prices are called particularly to the prices rose very fast simulbecause of, the great gold of interest averaged 5.3 not only than in any sub-

sequent, but also than in any previous period.

§ 6 The following table for Berlin displays the same connection between price movements and interest : — BERLIN

RATES

OF INTEREST IN RELATION AND FALLING PRICES? APPRECIA-

Bank

1851-1852 1853-1857 1858-1864 1865-1870 1871-1873 1874-1879 1880-1883 1884-1888 1889-1891 1892-1895 1896-1899

1900-1902 1903-1905

|MAarRKET|

TION OF Money IN CoMMODITIES

VIRTUAL

TO RISING

VIRTUAL

INTEREST IN| INTEREST IN |CoMMODITIES |COMMODITIES (Bank) (Market)

a

a

a

7

4.0 4.7 4.3 4.7 4.5 4.3 4.3 3.6 4.0 3.4 4.2 4.2 3.9

— as hare 4.0 4.1 3.2 3.4 2.5 3.1 2.2 3.6 3.2 3.0

= ds — 3.3 — 2.2 0.0 — 4,1 +3.1 — 0.1 a 7438) =.4 15a — 6.8 5.4 1.4

220) 1.4 ial — — — _ — = — = — —

)

— 1.5 4.0 0.0 6.3 3.3 5.4 1.8 7.4 — 3.2 8.6 1.6

1 This table is constructed from the data in the Appendix. The average in the second column marked (*) is for the years 1861-1864, T

THE

274

RATE

OF

[Cuar. XIV

INTEREST

In the foregoing table the relation between appreciation and interest is observed in seven out of twelve sequences

for bank rates (two being neutral) and in eight out of ten, for market rates. For France, index numbers covering a wide range of articles are not available. Using those given in the “ Aldrich Report” for sixteen articles, we have : — PARIS

RATES

OF INTEREST IN RELATION AND FALLING PRICES?

TO

RISING

APPRECIATION oF MONEY IN

CoMMODITIES

1861-1864 1865-1870 1871-1873 1874-1879 1880-1886 1887-1890 1891-1895

— + — + + —

8.1 3.6 4.5 4.3 2.3 5.1

Here the same connection is observed in five out of six sequences for bank rates and three out of four for market rates.” It will be noted that the course of prices and interest has been very much the same in England, Germany, and France. For New York we have the following table: — not 1858-1864. The “appreciation” to 1891 is calculated from the figures of Soetbeer and Heinz, as given in the ‘“ Aldrich Report”’ of 1893 of the U.S. Senate on Wholesale Prices. The figures for the later years are taken from The London Economist and from A. Soetbeer’s tables in the Journal of the Royal Statistical Society, Vol. LXVII, Part I, pp. 85, 89. + This table is constructed from the data in the Appendix. The average in the second column marked (*) is for the years 1872-1873, not 1871-1873.

? Assuming that prices fell, 1891-1895.

Sec.6]

NEW

INDUCTIVE

YORK

VERIFICATION

(MONETARY)

275

RATES OF INTEREST IN RELATION RISING AND FALLING PRICES}

a

ee

Cate

ee,

TO

ee

APPRECIAVv PRIME | TION fh I VIRTUAL ees 60 Two | Money IN Cnet 'N| CommopDays | Name Comroniice ee ITIES

_

|60 Days

ITIES

(60 Days)

(Prime)

t

t

a

j

j

5.4

1849-1857

:

E

== Ss)

1858-1860 1861-1865

e f

5 .

+ 6.4 — 20.2

1866-1874

:

:

===

— — 13.4

>

+ 4.7

12.2

1875-1879 1880-1884 1885-1891 1892-1897

: A ; :

+ + — +

7.9 0.6 0.2 5.6

13.0 6.0 4.9 10.2

1898-1906

J

— 3.5

1.1

We find here the same association of appreciation and interest in all of the three sequences for call loans, in two of the three cases for 60-day paper (the third being neutral), and in three of the six cases for “prime” paper (one being neutral). Perhaps the most remarkable feature of this table is the extremely low ratefor 1875-1879. Theextraordinary change in interest rates beginning in 1875 has been observed before; but its connection with the resumption act (as it seems to the writer) has been misconstrued.” 1 This table is constructed from the data in the Appendix. The rates of appreciation are calculated from Falkner’s figures for prices and wages in the “ Aldrich Report.” 2 Thus William Brough, referring to that act, says: ‘‘The mere announcement of our intention to put our money on a sound metallic basis had brought capital to us in such abundance that the resumption was not only made

easy, but the normal

rate of interest was

reduced. ... This remarkable reduction . . . is explainable only on the ground of a large reflux of foreign capital.” (Natural Law of Money, New York, 1894, p. 124.) If this explanation were correct, we would expect a still lower rate of interest after resumption had been accomplished; but the facts are the opposite.

276

THE

OF

RATE

INTEREST

[Cuap. XIV

§7 The preceding statistics apply to gold standard countries. The following table gives the rates of interest and appreciation for silver standard countries—India, Japan, and China :— RATES OF INTEREST FALLING PRICES SHANGHAI?

IN RELATION TO RISING IN CALCUTTA, TOKYO,

Bank

i

MARKET

APPRECIATION IN se CoMMODITIES

Calcutta, 1873-1875

5.3

+ 2.6

1876-1878 1879-1885 1886-1889 1890-1893

6.8 5.9 6.0 4.3

— 11.0 + 3.8 — 2.6 — 4.7

1873-1877 1878-1881 1882-1886 1887-1893 1894-1899 1900-1902

14.0 16.3 12.8 9.3 9.7 11.0

Shanghai, 1874-1881 1882-1888 1889-1893

9.1 7.5 7.0

Tokyo,

12.0 12:2 10.3 9.4 11.2 12.4

5.8* 5.8

AND AND

— 0.2 — 13.3 + 10.4 — 2.8 — 5.8 0.0 —1.4 +1.3 — 0.9

Here we find the theory confirmed in three out of four cases for India, three out of five for bank rates in Japan, and three out of five for market rates; one out of two for bank rates in China, while the one case for market rates is neutral. * This table is constructed from the data given in the Appendix. The entry marked (*) is for 1885-1888, not 1882-1888. See also ‘‘Price Movements and interest in Hedies by the writer, in Yale Review, May, 1897, p. 80.

Sxc. 8]

INDUCTIVE

VERIFICATION

(MONETARY)

277

Summarizing the cases for the seven countries examined we find 64 favorable and 22 unfavorable to the theory, distributed as follows: —

Favorable Unfavorable

The favorable cases are about three times as numerous as the unfavorable cases. This is a large preponderance, especially when we consider that there are so many causes affecting the rate of interest besides the mere appreciation or depreciation of the monetary standard. We therefore conclude with great confidence that, “other things being equal,” the rate of interest 1s relatively high when prices are rising and relatively low when prices are falling. § 8

The question now arises whether, on the average, the rate of interest fully adjusts itself to price-movements. This question cannot be answered with perfect certainty in any individual case, for the reason that we have no means

of knowing what the rate in commodities would have been had it been possible to have contracts drawn in “commodities” or in a monetary standard which was stationary with respect to commodities. We have, however, computed the “virtual”’ interest in commodities by adding to the rate of interest in money the rate of appreciation of money in commodities. Thus in London for 1826-1829 the rate of interest in money was 3.5 per cent., but money was appreciating relatively to commodities 4.2 per cent., so that the “virtual interest,”’ or interest actually paid, translated in terms of commodities (the forty commodities averaged

by Jevons), was 7.7 per cent.

It will be seen from the tables

that the virtual rate of interest reckoned in commodities:

278

THE

RATE

OF

INTEREST

[Cuap. XIV

usually varies inversely with the rate reckoned in money. For 1853-1857, money interest was 5.3 per cent., and for 1874-1879, 2.7 per cent.; but commodity-interest for 1853—

1857 was 2.9 per cent. and for 1874-1879, 7 percent. There are two possible explanations for this inverse relation. One is that when prices are rising the cause may not be monetary but may lie in a progressive scarcity of commodities produced and exchanged ; and, reversely, when prices are falling, the cause may lie in progressive abundance. From the theory of interest maintained throughout this book it follows that a progressive scarcity of commodities, implying as it does a progressive descending income curve, tends to make the rate of interest low; and reversely, progressive abundance, implying an ascending income curve, tends to make interest high. When, therefore, general price-movements represent changes in the income-stream of enjoyable services, the rate of ‘commodity interest”’ would naturally be high when prices were falling and low when prices were rising, whatever might be true of ‘“money-interest.” The second possible reason that commodity-interest and money-interest vary inversely during price-movements is that these movements are often imperfectly foreseen. The high or low rate in commodities is then an abnormal phenomenon. It is, as it were, a trick played by money on those who put too much faith in its stability. Thus,

during 1898-1905 the increase of prices in the United States is known to have been due largely to the increase of gold production. There is no evidence that commodities were getting scarce and incomes decreasing, but rather the reverse.

There seems, therefore, no reason

which would justify the low commodity-rate of interest of 1.8 per cent. which we found to have been virtually paid during that period. This low rate must, in all probability, have been due to inadvertence. The inrushing streams of gold caught merchants napping. They should have stemmed the tide by putting up interest, not only to 4.6 per cent., as

they did, but two or three per cent. higher.

Sc. 8]

INDUCTIVE

VERIFICATION

(MONETARY)

279

Doubtless both of the causes play a part in the explanation of particular cases. Sometimes commodity-interest is low during rising prices because it is foreseen that the real income-stream is then drying up, sometimes because it is not foreseen that monetary inflation is taking place, and sometimes for both reasons; and reversely, commodity-interest is high during falling prices, sometimes because of a foreseen increase of the income-stream, sometimes because of unforeseen contraction of the currency, and sometimes both.

It is impossible to decide what part these two factors — foreseen changes in real income and unforeseen changes in their monetary measure —may play in each individual case. We are too ignorant of the actual conditions behind the scenes. Nevertheless there is internal evidence to show that in general the latter factor — unforeseen monetary change —is the more important. This evidence consists in the fact that commodity-interest fluctuates so widely, in some cases even becoming negative. The following table shows that the mean variability or “standard deviation’’ from the mean, which is the best measure of the fluctuations of any variable, is far greater for the calculated or “ virtual” rate of interest than for the actual money rate of interest :— VARIABILITY (Standard Deviation) MARKET INTEREST

The times All strate

VIRTUAL INTEREST

virtual interest in commodities is from four to eight as variable as the market interest in money. these facts suggest —indeed, practically demon—that money-interest was not adequately adjusted

to the changes in purchasing power of money.

It is, of

course, not to be assumed that commodity-interest ought

280

THE

RATE

OF

INTEREST

[Cuar. XIV

to be absolutely invariable; but it is practically certain that its variations could not be three and a half times the variations in money-interest, unless the price-movements were inadequately predicted. If any doubts were possible on this point they must disappear when we find that for 1871-1873 commodity-interest in London was minus 2.5 per cent. This shows that money lenders would have been better off had they simply bought commodities in 1871 and held them until 1873. As it was, they actually lost something, measured in commodities, as a consequence of lending money. Such losses are especially apt to appear in short periods. Thus if we take the period 1824-1825, we find that the market rate was 3.7 per cent., the rate of appreciation was minus 14.5 per cent., and the virtual rate of interest in commodities, minus 10.8 per cent.! In New York during the inflation period, 1861-1865, commodity-interest sank to the ridiculously low figure of minus 13.4 per cent. This shows in a striking way how thoroughly the greenback inflation upset all business calculations, and how little the investing public realized in advance the serious rise in prices of those fateful years. That foresight was actually misguided at this time is amply confirmed if we examine the predictions as to the termination of the war and the reduction of the gold premium, which were recorded from month to month in the “Notes on the Money Market” in the (New York) Bankers’ Magazine. In all probability such errors of prediction are common in periods of paper money inflation. Our tables in § 7 show it for the Japanese inflation of 1878-1881. § 9

We can now understand why a high rate of interest need not retard trade nor a low rate stimulate it. These facts have puzzled many writers. For instance, Robert Baxter wrote : *— Journal of the Royal Statistical Society, June, 1876.

Sec. 9]

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VERIFICATION

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281

“Public inquiry has been of late strongly directed to the reasons for the very low rate of interest upon loanable capital in the year 1875, the more especially as ten years ago the very high rates then prevailing created equal surprise.”’

And Jevons wrote :!— “The effect of such and many more

changes effected during

the last twenty years or so is seen in a general increase in wealth and of mercantile industry and profits. Thus only can be explained the extraordinary high rate at which the interest of money has in the last ten years often stood. During 1854-1857 the rate of interest was only for a few months below 5 per cent., but for many months above it. For more than half a year it stood at 6 and 7 per cent., and in the end of 1857 it remained for nearly two months at 10 percent. Again, in 1861, interest rose to 6 and 8 per cent., and all this, to the surprise of the elder generation, without the general stoppage of trade, the breach of credit, and the flood of bankruptcy, which has hitherto attended such rates of interest. It is certainly not to increasing scarcity of capital we should attribute such rates, but rather to a greatly extended field for its profitable employment.”

But were these rates high? If we turn to our table for London rates, we find that the average market rate for 1853-1857 does appear to be the highest in the table; but, unmasking it of the money element, we find it is equivalent to a commodity-interest of 2.9 percent. Thisisa very low rate. Merchants with increasing prices and money profits would find it easy to repay loans on such a basis. Professor Bonamy Price,” writing at a time of very low

interest rates, says :— ““Eyvery one remembers the agitations associated with 7 per cent., the trepidation of merchants, the apprehension of losses in busi-

ness. ... If only a moderate rate could be reckoned on as steady, how happy would every one have been! ... Yet what are the facts and feelings to-day? Is every merchant, every manufacturer rejoicing in the pleasant terms on which he obtains the acAlas! no such commodation so necessary for his business? ... Commercial depression is the unisounds meet our ears. ... versal cry, depression probably unprecedented in duration in the annals of trade, except under the disturbing action of a prolonged (The italics are the present 1 Investigations in Currency, p. 95. Aaah writer’s.) (The italics 2 ‘One percent,” Contemporary Review, April, 1877. are the present writer’s.)

THE

282

RATE

OF INTEREST

[Caar. XIV

war. ... In the export figures, the writer still fails to see any signs of the long-looked-for revival of trade. Both quantities and values continue to shrink in all save a few cases. ... What, then, is the cause? The explanation will certainly not be found in gold nor in any form of currency whatever . . . nor has any one said anything so ridiculous. ... That cause is one and only one: overspending.”

If we turn back to the London table we find, however, that for 1874-1879 the commodity-rate of interest, so farfrom

being low, was7 per cent.! It would be astonishing if trade did not shrink under such a burden. All these writers mistook high or low nominal interest for high or low real interest. Tooke apparently did the same. In his History of Prices, Vol. II, p. 349, he names as the last of six reasons for the fall of prices for 1814-1837, “a reduction in the general rate of interest.”” This is probably not only an inversion of cause and effect, but also, when the veil of money is thrown off, a misstatement of fact. The commodity-interest for 1826-1829 was 7.7 per cent. Tooke, Price, and Jevons all overlooked the fact that interest, unlike prices, is not an instantaneous but essentially a time phenomenon. § 10

When long periods of price-movements are taken, the influence of appreciation on interest is more certain. The following table shows this for England. It consists of four periods, of 10, 12, 22, and 11 years respectively :— LONDON

MARKET RATES OF INTEREST IN RELATION TO RISING AND FALLING PRICES MARKET

APPRECIATION

INTEREST

INTEREST IN oF Money IN| CommMopiTIEs | CoMMODITIES

¢

VIRTUAL

7 te

1826-1835

41.2

aren

By

1874-1895

42.4

48

1853-1864

1896-1906

ae

at

Szc. 10]

INDUCTIVE

VERIFICATION

(MONETARY)

283

In averages covering so many years we may be sure that accidental causes are almost wholly eliminated. We find that during the period of falling prices, 1826-1835, the average rate of interest was only 3.4; that during the following period of rising prices, 1853-1864, it was higher (4.6 percent.) ; that during the next period, 1874-1895, when prices were again falling, the rate was again low (2.4 per cent.); and finally that in 1896-1906, with prices rising, interest again In every case interest is high when prices are recovered. rising and low when they are falling. For these long periods, therefore, we find the facts in agreement with the theory in every case. It is also a noteworthy fact that the commodity-interest in this table of long periods is far less variable than for short periods. The variability, as shown by the “standard deviation” of the four figures in the above table is, for London, .82 for the market rate, and 1.94 for the virtual rate. The adjustment of (money) interest to long price-movements 1s more perfect than to short price-movements. The following table gives the long time averages for New

York. NEW

The war period is omitted :— YORK

RATES OF INTEREST IN RELATION RISING AND FALLING PRICES INTEREST

Two

PRIME|

NaME

foipacd a

1849-1857

8.2!

APPREC ECIATI ON

Money IN

ComMMopITIES a — 3.8

OF

TO

Sivek i neen ner

IN COMMODITIES 7} 4.4

1875-1896

5.1

+ 2.6

7.7

1897-1906

4.5

— 34

1.1

We find that the money rate in the second period, when money was appreciating, was, as our theory requires, 1 The average of Elliott’s figures (which are not for “prime” paper) is 9.2, but 1.0 has been deducted from this average in order that it may be properly compared with the average of Robbins’s figures for 18751891. This correction is based on the fact that 1.0 was the average excess of Elliott’s figures over Robbins’s during the fifteen years, See Appendix to Chap. XIV, § 1. 1860-1874.

284

THE

OF INTEREST

RATE

[Cuap. XIV

lower than that in the first, when money was depreciating, but that the rate in the third period, when money was again depreciating, was, unfavorably to our theory, lower than that in the second when money was appreciating. Here we also see that the variability of the virtual interest in terms of commodities is less than for short periods, and more nearly like the variability for the market rate of interest in terms of money. The variability, as measured by the “ standard deviation,” of the rates of interest for the three periods in the above table are for market rate of interest in terms of money, 1.6; for virtual interest in terms of commodities, 2.3. § 11

Three general facts have now been established: (1) Rising and falling prices and wages are directly correlated with high and low rates of interest ;(2) The adjustment of interest to price-movements is inadequate; (3) This adjustment is more nearly adequate for long than for short periods. These facts are capable of a common explanation expressing the manner in which the adjustment referred to takes place. Suppose an upward movement of prices begins. Business profits (measured in money) will rise; for profits are the difference between gross income and expense, and if both these rise, their difference will also rise. Borrowers can now afford to pay higher “money-interest.”’ If, however, only a few persons at first see this, the interest will not be fully adjusted,’ and borrowers will realize an ‘It seems scarcely necessary to add as an independent cause of maladjustment the accumulation

(or in the opposite case, depletion) of bank reserves, for this is but another symptom of maladjustment due to imperfect foresight. An increase of gold supply, as in 18521853 (see Tooke and Newmarch, History of Prices, Vol. V, p. 345), may first find its way into the loan market instead of into circulation. But if foresight were perfect, this would not happen, or if it did happen, borrowers would immediately take it out (or increase the liabilities against it) to avail themselves of the double advantage of low interest and high prospective profits from the rise of prices about to follow.

Sc. 12]

INDUCTIVE

VERIFICATION

(MONETARY)

285

extra margin of profit after deducting interest charges. This raises an expectation of a similar profit in the future and this expectation, acting on the demand for loans, will raise the rate of interest. If the rise is still inadequate, the process is repeated, and thus by continual trial and error the rate approaches the true adjustment. When a fall of prices begins, the reverse effects appear. Money profits fall. Borrowers cannot afford to pay the old rates of interest. If, through miscalculation, they still attempt to do this, it will cut into their real profits. Discouraged thus for the future, they will then bid lower rates. Since at the beginning of an upward price-movement the rate of interest is too low, and at the beginning of a downward movement it is too high, we can understand not only that the averages for the whole periods are imperfectly adjusted, but that the delay in the adjustment leaves a relatively low interest at the beginning of an ascent of prices, and a relatively high interest at the beginning of a

descent.

And this is what we find to be true.

That the

adjustment is more perfect for long periods than for short seems to be because, in short periods, the years of non-adjustment at the beginning occupy a larger relative part of the whole period.

§ 12 What has been said bears directly on the theory of “ credit cycles.” In the view here presented, periods of speculation

and depression are the result of inequality of foresight. If all persons underestimated a rise of price in the same degree, the non-adjustment of interest would merely produce a transfer of wealth from lender to borrower. It would not influence the volume of loans (except so far as the diversion of income from one person to another would itself have indirect effects, such as bankruptcy). Under such circumstances the rate of interest would be below the normal, but as no one would know it, no borrower would

286

THE

RATE

OF

INTEREST

[Cuar. XIV

borrow more and no lender lend less because of it. In the actual world however, foresight is very unequally distributed. Only a few persons have the faculty of always “coming out where they look.’ Now it is precisely these persons who largely make up the borrowing class. Just because of their superior foresight, there is delegated to them the management of capital; they become “captains of industry.” It therefore happens that when prices are rising, borrowers are more apt to see it than lenders. Hence, while the borrower is willing to pay a higher interest than before for the same loan, lenders are willing to loan for the same interest as before. This disparity has as its effect that the rate of interest will not rise as high as if both sides saw the conditions equally well. It will also cause an increase of loans and investments.’ This constitutes part of the stimulus to business which takes place in times of rising prices. When prices fall, on the other hand, borrowers see that they cannot employ “money” productively except on easier terms, but lenders do not see why the terms should be made easier. In consequence, “enterprisers’”’ borrow less, trade languishes, and, though interest falls in consequence of decrease in demand, it does not fall enough to keep the demand from decreasing.” We see, therefore, that while imperfection of foresight transfers wealth from creditor to debtor or the reverse, inequality of foresight produces overinvestment during rising prices and relative stagnation during falling prices. ? That this and the corresponding statement in the next paragraph are borne out by facts appears to be confirmed, so far as bank loans and discounts are concerned, by Sumner, History of Banking in the United States (New York, 1896), and Juglar, Crises Commerciales (Paris, 1889). ? President Andrews, in An Honest Dollar, p. 3, writes: ‘Interest is low . . . not because money is abundant as before, but because it is not, its scarcity having induced fall of prices, and so paralysis in industry.” But, it should be added, the cause of the fall of interest is primarily the expectation of small profits.

Sxc. 13]

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VERIFICATION

(MONETARY)

287

In the former case society is trapped into devoting too much investment of productive energies for future return, while in the contrary case, underinvestment is the rule. It does not seem possible to decide the question which of the two evils is the greater. § 13

The facts which have been shown in this chapter are important in two respects. They prove, first, that men do actually, even if unaware of so doing, contrive to offset the effects of changes in the monetary standard by adjusting the rate of interest; and, secondly, that this adjustment is far from adequate. In consequence of the inadequacy of the interest-adjustment, a large amount of wealth is continually and unintentionally transferred from the creditor- to the debtor-class, and vice versa. The bimetallists were partially right in their claim that the creditorclass were gainers during the period of falling prices in the two decades 1875-1895. The situation has been the exact opposite during the decade 1896-1906. We must not make the mistake, however, of assuming that the enrichment of the debtor-class during the last decade atones for the impoverishment of that class during the previous two decades; for the personnel of social classes changes 1 For arguments on both sides, see Professor Marshall’s evidence,

Report on Depression of Trade (1886), p. 422. See also his Principles of Economics, Vol. I (3d ed., 1895), p. 674: ‘‘When we come to discuss the causes of alternating periods of inflation and depression of commercial activity, we shall find that they are intimately connected with those variations in the real rate of interest which are caused by changes in the purchasing power of money. For when prices are likely to rise, people rush to borrow money and buy goods, and thus help prices to rise; business is inflated, and is managed recklessly and wastefully; those working on borrowed capital pay back less real value than they borrowed, and enrich themselves at the expense When afterwards credit is shaken and prices of the community. begin to fall, every one wants to get rid of commodities and get hold of money which is rapidly rising in value; this makes prices fall all the faster, and the further fall makes credit shrink even more, and

thus for a long time prices fall because prices have fallen.”

288

THE

RATE

OF

INTEREST

[Cuap. XIV

rapidly. Nor must we make the mistake of assuming that the debtor-class consists of the poor. The typical debtor to-day is the stockholder, and the typical creditor, the bondholder. What is actually going on to-day in consequence of a steadily cheapening dollar is a vast transfer of advantage from bondholders to stockholders. It is this transfer which has produced many of our latest millionaires. Their millions have been silently abstracted from the pockets of the unsuspecting “safe” investors in bonds, depositors in savings banks, and the salaried classes. The fault, however, is not of those who thus profit, but of the monetary conditions which permit the ceaseless ebb and flow of price-levels. The problem of a stable monetary standard is of vital importance. We are apt to forget its importance during a period of “prosperity,” and we are apt also to forget that much of what is called prosperity is delusive. It is delusive for two reasons: First, it is often not general prosperity, but prosperity of the debtor or stockholding or entrepreneur classes, who are always much in evidence, at the expense of the creditor, bondholding, salaried classes, who bear their losses silently

behind the scenes;

secondly, so-called prosperity is often

another name for reckless wastefulness, for which there must

be a day of reckoning in the form of a commercial crisis.’ See The Gold Supply and Prosperity, edited by Byron W. Holt (The Moody Corporation), New York, 1907.

CHAPTER

XV

INDUCTIVE VERIFICATION

(ECONOMIC)

§ 1

In the last chapter we found statistical evidence of the influence of changes in the monetary standard upon the rate of interest. We now proceed to a similar inductive study of the economic —as distinct from the monetary — influences upon the rate of interest. In a study so broad, it would be useless to attempt any exhaustive verification by statistics; the facts at hand are too meager, and not such as to enable us to isolate the separate causes at work. It will usually happen in any given case that some of the economic causes tending to make interest high are combined with others which tend to make it low. The fact, therefore, that interest is either high or low in such a case will not, of itself, be decisive in favor of any theory. The best that we can expect is to show that the facts as we find them are at any rate consistent with the theory maintained. For practical purposes, such a showing is enough, both because the theory should stand on its own merits as an analysis, without the bolster-

ing of statistical verification; and because, if the analysis were really incorrect, a very cursory examination of the facts would probably suffice to refute it. In our study of facts it is well to remember that the causes

tending to make interest high or low sometimes work out their effects, partly or wholly, in other ways. For instance, the economic causes which, in the United States, have

tended to make interest high, have also tended to bring in loans from other countries, such as Great Britain, where the rate of interest was low. The introduction of the loans prevented interest from being as high as it otherwise would. U

289

290

THE

RATE

OF

INTEREST

[Coap. XV

In general it is true that a cause which would tend to make interest high in a community may simply result in increasing the loans contracted by that community, provided there exists another community in which the rate of interest is lower. If recourse to borrowing is not practicable, other methods of adding to present at the expense of future income —of “tipping forward” the income curve —may be found. If this “tipping forward”’ goes far enough it will show itself in a dissipation of capital; if not, in a slower accumulation. Contrariwise, the causes which work toward lending may, if lending is impracticable, result in some other form of “ tipping back” the income curve and may show itself in a more rapid accumulation of capital or a less rapid dissipation. Finally, the same economic causes which tend to make interest high will tend also to encourage the production of the less substantial and durable instruments, whereas those causes which tend to make interest

low will favor the production of instruments of the more durable and substantial types. In short, in our collection of facts we should ascribe very similar significance to the four sets of phenomena — high interest, borrowing, disstpation of capital, and perishabtlity of instruments ; any causes back of these phenomena, which, according to our theory, should produce any one of the four, will tend also to produce the other three. Likewise we should ascribe similar significance to the four opposing phenomena —low interest, lending, accumulation, and durability of instruments.

§ 2 Briefly stated, the theory we are testing is that the rate of interest expresses human preference for present over future goods, as that preference works itself out from the nature of the individual and the character of his income-

stream.

We shall begin by considering the manner

in

which the nature of the individual influences the rate of interest.

Sec. 2]

INDUCTIVE

VERIFICATION

(ECONOMIC)

291

In a previous chapter we enumerated the causes which, in the nature of man, tend to make interest high or low. It was there maintained that foresight, self-control, and regard for posterity tend to make interest low. We may therefore expect to find, in a community possessing these qualities, one or more of the four interequivalent phenomena already mentioned —low interest, lending to other communities, accumulation of capital, and construction of substantial instruments;

and to find, in a community lacking

these qualities, one or more of the four opposite conditions. No extended study is needed to show that precisely these opposing sets of phenomena are actually found in the two opposite conditions mentioned. The communities and nationalities which are most noted for the qualities men-

tioned — foresight, self-control, and regard for posterity — are probably Holland, Scotland, England, France, and the Jews, and among these peoples interest has been low. Moreover, they have been money lenders, they have the habit of thrift or accumulation, and their instruments of wealth are in general of the substantial variety. The durability of their instruments is especially obvious in their buildings, both public and private, and in their ways of transportation

— carriage roads, tramways, and railroads.

Thus in Eng-

land the railways have expended an average of $165,000

per mile, which is from two to three times the corresponding expenditure in most countries. The difference, though partly explainable by a difference in methods of accounting, seems largely due to the lower rate of time-preference in England. John Rae observes of Holland :— “The Dutch seem, of all European nations, hitherto to have been inclined to carry instruments to the most slowly returning orders. The durability given to all the instruments constructed by them, 1 See Dorsey, English and American Railroads Compared, New York (Wiley), 1887; Price Howell, Journal of the Royal Statistical Society, Vol. LXII, p. 83; Commercial and Financial Chronicle,

Vol. LXXIV, p. 1224.

292

THE

RATE

OF INTEREST

[Coar. XV

the care with which they are finished, and the attention paid to preserving and repairing them, have been often noticed by travel-

In the days when their industry and frugality were most ers. remarkable, interest was very low, government borrowing at 2 per cent., and private people at 3.”

On the other hand, among communities and peoples noted for lack of foresight and for negligence with respect to the future are China, India, Java,? the negro communities in the Southern states, the peasant communities of Russia,’ and the North and South American Indians, both before

and after they had been pushed to the wall by the white man. In all of these communities we find that interest is high, that there is a tendency to run into debt and to dissipate rather than accumulate capital, and that their dwellings and other instruments are of a very flimsy and perishable character. It may well be that there are other causes at work to

produce these results.

We are here merely noting the fact

that lack of foresight is one factor present. Of China, Rae states :— “The testimony of travelers ascribes to the instruments formed by the Chinese a durability very inferior to similar instruments constructed by Europeans. The walls of houses, we are told, unless of the higher ranks, are in general of unburnt bricks of clay, or of hurdles plastered with earth; the roofs, of reeds fastened to laths. We can scarcely conceive more unsubstantial, or temporary fabrics. Their partitions are of paper, requiring to be renewed every year. A similar observation may be made concerning their implements of husbandry and other utensils. They are almost entirely 1 The Soctological Theory of Capital, pp. 128-129. ? My colleague, Professor Clive Day, informs me that the rate of interest in Java is often 40 per cent. * See Bloch, The Future of War, p. 205. It appears that the peasant will sell a promise to labor a short time in the future at one third the current wages! See also E. B. Lanin (pseud.), “Russian Finance,” Fortnightly Review, February, 1891, Vol. LV, pp. 188, 190, 196, for typical and extreme cases. Inostranietz, ‘‘L’Usure en Russie,’ Journal des Economiste, 1893, Ser. 5, Vol. XVI, pp. 233-243, states that the rates paid by poor peasants to well-to-do peasants are frequently 5 per cent. per week!

Sec.2]

INDUCTIVE

VERIFICATION

(ECONOMIC)

293

of wood, the metals entering but very sparingly into their construction; consequently they soon wear out, and require frequent renewals.”’ ! “European travelers are surprised at meeting . . . little floating farms, by the side of swamps which only require draining to render them tillable. It seems to them strange that labor should not rather be bestowed on the solid earth, where its fruits might endure, than on structures that must decay and perish in a few years. The people they are among think not so much of future years as of the present time.’’? “The Father Parennin, indeed, asserts, that it is their great deficiency in forethought and frugality in this respect, which is the cause of the scarcities and famines that frequently occur. ‘I believe,’ he says, ‘that, notwithstanding its great number of inhabitants, China would furnish enough grain for all, but that there is not sufficient economy observed in its consumption, and that they employ an astonishing quantity of it in the manufacture of the wine of the country, and of raque.’”’ ® “In China, we are told by Barrow, that the legal rate of interest is 12 per cent., but that, in reality, it varies from 18 to 36.” 4

Simcox writes of China as follows :— “The legal maximum is 3 per cent. per mensem, and the usual rate, as already mentioned, 30 per cent., per annum.’’®

Even on the seacoast where Englishmen have settled, the rate of interest is high, and its reduction, such as has occurred, is only because of the equivalent economic

phenomenon, loans from abroad. These facts are seen in the Appendix,® where the rates of interest in China are given. It is interesting to observe how the economic conditions in China which at first produced high interest afterward led gradually to loans from England and a fall in the rate of interest. The bank rate in Shanghai as given in the table was at first (1866) 13 per cent., and gradually fell to 6 per cent. as investments of English capitalists were made. 1 The Sociological Theory of Capital, pp. 88-89. 7” Loc. cit., p. 92. 4 Loc. cit., p. 128. 3 Loc. cit., pp. 89-90. 5 Primitive Civilizations, London (Swan Sonnenschein), 1894, Vol. II, p. 327. ® See Appendix to Chap. XIV, § 1.

THE

294

RATE

OF INTEREST

[Cuar. XV

Of the North American Indians, Rae observed :— “Upon the banks of the St. Lawrence, there are several little Indian villages. They are surrounded, in general, by a good deal of land from which the wood seems to have been long extirpated and have, besides, attached to them, extensive tracts of forest. The cleared land is rarely, I may almost say never, cultivated, nor are any inroads made in the forest for such a purpose. The soil is, nevertheless, fertile, and were it not, manure lies in heaps by their houses.

Were every family to inclose half an acre of ground,

till it, and plant in it potatoes and maize, it would yield a sufficiency to support them one half the year. They suffer too, every now and then, extreme want, insomuch that, joined to occasional intemperance, it is rapidly reducing their numbers. This, to us, so strange apathy proceeds not, in any great degree, from repugnance to labor; on the contrary, they apply very diligently to it, when its reward is immediate.” !

Of the South American Indians in Paraguay Rae tells of the difficulties which the Jesuits found in persuading the natives to provide for the future :— 4 . if these [the Jesuits] gave up to them the care of the oxen with which they plowed, their indolent thoughtlessness would probably leave them at evening still yoked to the implement. Worse than this, instances occurred where they cut them up for supper, thinking, when reprehended, that they sufficiently excused themselves by saying they were hungry.” ?

In regard to the negro and the Russian we may cite the statistics of George K. Holmes* and the observations of N. T. Bacon.* §3

In many if not all of the cases which have been cited there are, of course, other elements which would tend to explain the facts besides mere mental characteristics. Thus, the high rate of interest among the negroes and the Russian peasants is undoubtedly due in part to their pov1 The Sociological Theory of Capital, pp. 71-72. 2 Loc. cit., p. 76. 3 Census of 1890.

“ Yale Review, Vol. XII, pp. 141, 239; Vol. XIII, p. 51.

Src. 3]

INDUCTIVE

VERIFICATION

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erty, though their poverty is in turn largely due to the mental characteristics. There is here in operation the vicious circle which has been noted in Chapter XII. Where there is too little appreciation of the needs of the future, capital tends to disappear; and the pressure of poverty tends to enhance still further the demands of the present and to press down its victims from bad to worse. But there are not wanting cases in which even persons who have wealth, but who nevertheless lack foresight and selfcontrol, exhibit the same facts, especially by running into debt. This is characteristic of a considerable number of the spoiled sons of rich English noblemen. The type is well described in some of Stevenson’s novels. These persons are found living in Australia and elsewhere in virtual

exile on a stipend provided by their families at stated intervals. This stipend is sometimes provided on condition that they remain away from their original environment with

its temptations

to extravagance.

One such individual

known to the writer had inherited a large fortune. The precaution had been taken to leave it in trust so that he could draw only the income. Yet this man contrived to contract large debts on chattel mortgages at high rates of interest, and was noted for his wasteful, short-sighted erection of temporary dwellings in the various communities among which he continually flitted. The same characteristics are often found among wealthy students at universities, who have acquired, through improper home training,

an exaggerated idea of the needs of the moment and little appreciation of those of the future. These men become the victims of money lenders, and are frequent patrons of the pawn shops. Not only do we find examples of a high rate of preference for present over future goods among the prodigally rich, but we often find the opposite example of a low rate of preference for present over future goods among the thrifty poor. Examples are especially frequent among the Jews,

whose propensity to accumulate and to lend money even

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in the face of misfortune and social ostracism, is too well known to require extended comment.

§4 The factor which has been designated as “regard for posterity”’ deserves special attention. Perhaps the most conspicuous example of extreme disregard for posterity is found in Rome during the time of its decline and fall. The following quotations from Rae contain important testimony : — “Tt were needless,” he says, “to enlarge on a subject so well known as that of the general corruption of Roman manners, from the time of the first Cesar. Venality and licentiousness may be said to have been universal. I shall confine myself to one particular, as marking sufficiently the declension of those principles on which the strength of the effective desire of accumulation mainly depends. I allude to the decay of the family affections, of which evidence everywhere meets us. The men did not wish to be fathers, scarcely did the women wish to be mothers. . . They lived, not in others, or for others, but for themselves, and sought their good in enjoyments altogether selfish. It was their aim to expend on their own personal pleasures whatever they possibly could. It would seem as if the majority, could they have foreknown the exact limits of their lives, would have made their fortunes and them terminate together. As they could not do so, the fortunes of many ended before their lives, as the fortunes of others held out beyond their lives. To reap, however, themselves, while alive, all possible benefit from what they might chance to leave others to enjoy after their death, they encouraged some of the members .of a despicable class who seem to have constituted no inconsiderable part of Roman society. Parasites ready to minister to every pleasure, and to perform every possible service, waited on the man of wealth, in the hope and expectation of enjoying a portion of it after his death. They were more desirable than children, both because they were able to give something more than mere unsubstantial affection and esteem, and because they were willing to give it.... It gave occasion to the law compelling parents to leave their children a certain part, a fourth, of their property, Its prevalence may be judged of by the wording of the enactments increasing the children’s share. ... The general selfishness of the principles guiding the conduct of individuals, may be gathered

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from the prevailing proverb, “When I die let the world burn.” . . . Pasture took place of tillage; corn was brought from the provinces; and when the supply failed famine ensued. Even the construction of ships for the transport of this, and other merchandise, would seem to have been an effort to which the accumulative principle was scarcely equal. It was found necessary to encourage it by rewarding those who prosecuted that branch of industry. Sometimes land formerly cultivated was allowed to lie entirely waste, and passed altogether out of the class of instruments. The forest and wilderness gained on the Romans, as they would now, for similar reasons, on an Indian population, were some of these tribes put in possession of the domains, anciently the property of their race, at present yielding abundantly to the provident industry of the whites. Had there been no interruption of the barbarians, the Empire must have perished, more slowly perhaps, but as certainly, from the operation alone of these internal causes of decay. They were occasioning a progressive diminution of the capacity which materials formerly possessed. Thus, it is to the Romans themselves as much as to the barbarians, that the destruction of the public edifices is to be ascribed. The stones were applied to private purposes.”’ ? “Thus, among the Roman writers, the heir is always represented in an invidious light, and to save for him is represented as a folly. The writings of Horace, and the contemporary poets, throughout, exemplify the prevalence of this feeling.” ? “Tn ancient Rome, interest was in reality exceedingly high, from 12 to 50 per cent.” §

These rates doubtless refer to the degenerate days. Previously, at the time of the end of the republic, the rate was as low as 4 to 6 per cent.*

§ 5 The characteristics of foresight, self-control, and regard for posterity seem to be partly natural and partly acquired within the lifetime of the individual. Among the cases 2 Loc. cit., p. 64. 1 Loc. cit., pp. 95-99. Rae’s authority is Boucher’s Histotre de L’ Usure, 8 Loc. cit.,p.129. Paris, 1819, p. 25. 4 See Seligman’s Principles of Economics, New York (Longmans),

1905, p. 404.

THE

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which have been given are conspicuous examples of both, although it is difficult here, as always, to disentangle the influence of nature from that of environment. We are accustomed, for instance, to ascribe to the Jews a natural racial tendency to accumulate, though this characteristic is certainly reénforced by, if not entirely due to, the extraordinary influence of Jewish tradition. Of the Scotch, it would be difficult to say how much of their thrift is due to nature and how much to training handed down from

father to son.

The American negro is regarded by nature

as a happy-go-lucky creature; but recent experience with industrial schools has demonstrated the fact that these characteristics can be largely reversed by training, if in fact they have not been entirely created by the lack of

training under conditions of slavery. There is now accumulating much testimony * to show that there is more error than truth in the common opinion as to the relatively great importance of heredity as compared with environment.

When postal savings banks were first introduced in England, it was objected that the habits of the English poor, for whom they were intended, were such that they would never make use of them. But Gladstone insisted that habits

were an arbitrary matter, and that the fashion of spending could be displaced by the fashion of saving as soon as the principle of imitation had had time to operate. The experience with English postal savings banks has justified his prediction.? In fact, it would be a serious mistake to assume that the characteristics of man as to foresight, self-control, and regard for his own and his children’s future are fixed racial or national qualities. The part which nature may play in For instance, the reports of the Children’s Aid Society of New York; the child-saving work of Dr. and Mrs. J. H. Kellogg at Battle Creek; the evidence of the British Interdepartmental Committee on School Children, etc.

* See The Development of Thrift, by Mary W. Brown, New York

(Macmillan),

1900.

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these matters is as yet far from being understood; but however great that part may be, it is certainly true that the influence of training is also great, and therein lies the possibility and hope of social reform in these matters. It should be one of the distinct aims of any intelligent modern education, whether in the home or the school, to inculcate foresight, self-control, and a due regard for the needs of future years and even of future generations. It goes without saying that individuals and nations with these characteristics have therein a more secure and permanent claim for success in all directions.

§ 6 But, as has been emphasized in previous chapters, the rate of preference for present over future goods is not a question of mere personal characteristics, but depends also upon the character of one’s income-stream; namely, on its size, shape, composition, and probability. In respect to size, our theory maintains that the larger the income, other things such as foresight and selj-control being equal, the lower the rate of preference for present over future goods. If this is true, we should expect to find poverty and riches associated respectively with a high and a low rate of interest, or with borrowing and lending, or with spending and saving, or with perishable and durable instruments. That this char-

acterization is in general correct is not likely to be denied. It is true of course that the amount loaned to the poor is small because each individual loan is necessarily small; but the number of these loans is very great, and the desire of the poor to borrow, when it exists, is very intense. The many conspicuous exceptions to these rules are explainable on other grounds. It not infrequently happens that the poor, instead of being borrowers, are lenders; but in this case either they have unusual foresight, self-control, regard for their children, and other qualities tending in the same direc-

tion, or else their income-stream has such a time-shape

300

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as to encourage lending rather than borrowing. Reverse conditions apply likewise to the case of many wealthy men, viz. those who are borrowers rather than lenders. Whether from wrong training or other causes, they lack foresight, selfcontrol, regard for posterity, etc. But disregarding these factors and confining our view to the direct influence of the size of income, it is true, in a general way, that the poor are more eager borrowers than the rich, and will often patronize pawn shops and other agencies in which the rate of interest is inordinately high; also that their dwellings or other structures are often of a very unsubstantial character, such as would not “pay” except to those who put a very high estimate on present as compared with future goods. The deeper the poverty, the higher the rates which the borrowers are compelled to accept. Even pawnbroking is not available for the extremely poor, but is patronized rather by the moderately poor. Those who are extremely poor cannot give the kind of security which the pawnbroker requires. On this account they become the victims of even higher rates of interest, pledging their stoves, tables, beds, and other household furniture for the loans they contract. These loans are repaid in installments

such that the rate of interest is seldom lower than 100 per cent. per annum.’ Turning from classes to countries, it is noteworthy that in the countries in which there are large incomes we find low interest, a tendency to lend rather than borrow, accumulate rather than spend, and to form durable rather than perishable instruments, whereas in countries where incomes are low the opposite conditions prevail. Thus, incomes are large and interest is low in Holland, France, and England, whereas the reverse conditions hold in Ireland, China, India, and the Philippines. In Ireland, for instance, especially ‘For details as to thirteen typical loans of this character, see U. S. Bureau of Labor Bulletin, No. 64, May, 1906, pp. 622-633. Thus, “loan 1,” 143 per cent., “loan 3,” 224 per cent., “loan 7,” 156 per cent.

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in the early part of the nineteenth century, the rate of interest was high. The cottier was always in debt, and his hut and other instruments were of the most unsubstantial variety. Again in the Philippines the rates of interest on good security are often 2, 5, and even 10 per cent. a month. “The Chinese money lender frequently takes advantage of the Filipino’s poverty.”? Many of these cases may be wholly or partly explained by other causes such as have been mentioned in the last section. The possibility of more than one explanation shows that in this field we can scarcely hope to adduce any complete proof of an inductive nature. But since any of the possible explanations fit in with our theory, we are safe in saying that the facts do not at any rate contradict that theory.

7 As to the influence of the composition of income, it is even more difficult to obtain any statistical confirmation of value. In a previous chapter it was shown that variations in the amount of that income which takes the form of food would have an effect on the rate of interest similar to the effect of variations in the total income itself. Scarcity of food should therefore cause high interest, and abundance of food, low interest. Certain presumptive evidence is found in the observation of Jevons on the relation between the price of wheat and the rate of discount.*? Wheat being the most typical food in England, it may be assumed with considerable probability that its price varies inversely with the amount of food consumed. Jevons found that a 1See Longfield, ‘The Tenure of Land in Ireland,” in Proloyn’s Systems of Land Culture, London (Cassell, Petter, and Galpin), 1876, . 16. 7 2 From a letter to the author from Professor E. W. Kemmerer; see also his article in The Business Monthly, Pittsburg, April, 1907, p. 2. 8 See Investigations in Currency and Finance, 1884, p. xiv; also, Robert Goodbody, in Byron W. Holt’s Gold Supply and Prosperity, p. 166.

302

THE

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[Caar. XV

high price of wheat corresponded to high rates of interest, and vice versa. This would almost amount to saying that a relative scarcity of food was associated with high interest, and vice versa. During the siege of Paris the rate of interest was high, although other causes than the scarcity of bread were doubtless accountable for the fact. § 8 As to the influence of risk, we encounter similar difficulties. But evidence as to our main contention, namely, that in general risk tends to raise the commercial rate of

interest but to lower pure interest, is forthcoming. The first part of this proposition is a matter of so common observation that no special collection of facts is necessary. Every lender or borrower knows that the rate of interest varies directly with risk. A bird in the hand is worth two in the bush. The principle applies not only to the

explicit interest in loan contracts, but to the implicit interest which goes with the possession of all capital. Where there is uncertainty whether capital saved for the ‘future will ever be of service, but there is certainty that it can be of service if used immediately, the possessor needs the possibility of a very high future return in order to induce him to save the capital for future use. It is noteworthy that in time of war there is a ruthless destruction of crops and a tendency among the possessors of consumable wealth to enjoy it while they may. The same conditions are characteristic of communities which are in a perpetual state of uncertainty.’ ‘ The rate of interest is everywhere

proportional to the safety of investment. For this reason we find in Korea that a loan ordinarily brings from 2 to 5 per cent. per month. Good security is generally forthcoming, and one may well ask why it is so precarious to * On the uncertainties of Indian life, see The Sociological Theory of Capital, pp. 69, 70.

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lend.

The answer is not creditable to Korean justice. In a land where bribery is almost second nature, and private rights are of small account unless backed up by some sort of influence, the best apparent security may prove a broken reed when the creditor comes to lean upon it.’’ 4 There remains the second part of the proposition in regard to risk; namely, that while risk tends to increase the rate of interest on risky loans, it tends at the same time to decrease that on safe loans. This proposition is not familiar to most persons. It has usually caused surprise when, during a time of political stress and danger, the rates of interest on perfectly safe loans were found to be so small. Many such instances may be cited. At certain periods during the Civil War, when the greatest uncertainty prevailed, loans with good security were contracted at nominal rates, and bank deposits tended to accumulate for lack of sufficient outlet in secure investments. Times

when public confidence is shaken are characterized not only by high rates on unsafe loans, but by efforts on the part of timid investors to find a safe place for their savings, even

if they have to sacrifice some or all of the interest upon it. They will even hoard it in stockings and safe deposit vaults, or leave it idle on deposit in bank. “... In 1903... the public took alarm and began to hoard their capital

in the form of banking credits, instead of bidding with it for securities. In the meantime, the scarcity of free capital in the market enabled the banks, which held the money of the public, to exact 5 and 6 per cent.” ? We may even occasionally find cases in which the desire to obtain a safe method of using capital is so keen and so difficult to satisfy that the rate of interest is negative. The investor is then in the position of the user of a safe deposit vault, thankful enough to receive the assurance that his capital, by being 1H. B. Hurlbert, The Passing of Korea, New York, 1906, p. 283.

2 Charles A. Conant, “How the Stock Market reflects Values,” North American Review, March, 1905, pp. 346-359.

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[Cuar. XV

intrusted to another, will not be diminished, to say nothing of being increased.’ § 9

We still need to verify the most essential part of our theory; namely, that the rate of interest depends upon the time-shape of the income-stream. If the theory is correct, we should find, other things being equal, that when, in any community, the income-streams of its inhabitants are increasing, the rate of interest will be high; that when they are decreasing, the rate of interest will be low; and that when they alternate from one condition to the other, the

rate of interest will also alternate according to the period of the loan. The most striking examples of increasing income-streams are found in new countries. It may be said that the United States has almost always belonged to this category. Were it possible to express by exact statistics or diagrams the size of American incomes, they would undoubtedly show a steady increase since colonial days. Statistics almost equivalent to these desiderata are available (though not very accu-

rate) in the form of the United States Census figures of “ner capita wealth,” as well as statistics of production and consumption of staple commodities and of exports and imports. These, combined with common observation and the statements of historians, lead to the conclusion that American incomes have been on the increase for two hundred years. It is also true that during this period of rising incomes, the rate of interest has been high. The

simplest interpretation of these facts is that Americans, being constantly under the influence of great expectations, have been always ready to promise a relatively large part of their abundant future income for a relatively small addition to their present, just as he who expects soon to * See Bagehot, Lombard Street, Chap. VI; also, Macaulay, History of England, Chap. XIX.

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come into a fortune wishes to anticipate its realization by contracting a loan. Not only has the rate of interest been high in America as compared with other countries during this period of ascending incomes, but some of the other conditions equivalent to a high rate of interest have also been in evidence. Thus, the country has been conspicuously a borrowing The proceeds of country, in debt to other countries. such loans have shown themselves in increased imports and diminished exports, creating a so-called unfavorable balance of trade. These phenomena have usually been expressed as a “demand for capital”;

but, while it is quite

true that the exploitation of our natural resources required the construction of railways and other forms of capital, this fact is better and more fully expressed in terms of income. We wanted, not the railways and machinery themselves, but the future enjoyable products to which this apparatus led. The construction of these instruments necessarily diminished the immediate enjoyable income of the country and added to that of the expected future. It was to even up this disparity of immediate and remote income that loans were contracted. It does not matter whether the loans from the foreigner were received in the form of machinery and other instruments of production, or in the form of the comforts of life to support us while we ourselves constructed the instruments. In either case the essential fact is the transformation of the income-stream, and not the “need of capital,” which is merely one of the means thereto. Import statistics show that, as a matter of fact, we received our loans from the foreigner in both forms. Not only have we witnessed the phenomena of high rates of interest and of borrowing during this period of American development, but it is also true that the character of the instruments created was for the most part of the unsubstantial and “quickly returning” kinds. Our highways, as John Rae pointed out, were little more than the natural x

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[Coar. XV

surface of the earth after the removal of trees and rocks; our railways were lightly ballasted, often “narrow gauge,” and crooked to avoid the necessity of excavations and tunnels; our earliest buildings were rude and unsubstantial. Everything was done, not in a permanent manner with reference to the remote future, but in order to save a large first cost. During the last two decades these conditions have been

reversed. The rates of interest in America have fallen greatly, as the statistics in the Appendix will show. We have ceased to be a borrowing nation, and are buying back our securities from abroad. This repayment of debts is accomplished through the export of our now abundant products, and creates a so-called favorable balance of trade. Again, the character of the instruments which have been now for some time in process of construction is of the most substantial kind. Steel rails have long since taken the place

of iron rails, “broad gauge” of “narrow gauge ”’; railways have been straightened by expensive tunnels, by bridges, and by excavations;? dwellings and other buildings have been made more substantial; macadamized roads are gradually coming into vogue; and in every direction — industrial, agricultural, and domestic — there is an evident tendency to invest a large first cost in order to reduce future running expenses. § 10 Thus in America we see exemplified on a very large scale the truth of the theory that a rising income-stream raises and a falling income-stream depresses the rate of interest, or that these conformations of the income-stream work out their effects in other equivalent forms. A similar causation may be seen in particular localities in the United States, es? See Appendix to Chap. XIV, § 1. 7 It is estimated that Western railways in the United States have actually under way or in contemplation improvements amounting Wall Street Journal, December 19, 1905. to $1,000,000,000.

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pecially where changes have been rapid, as in mining communities.

In California, in the two decades between 1850

and 1870, following the discovery of gold, the income-stream of that state was increasing at a prodigious rate, while the state was isolated from the world, railroad connection with

the East not being completed until 1869. During this period of isolation and ascending income, “. . . opportunities for investment were innumerable. Hence the rates of interest were abnormally high. The current rates in the ‘early days’ were quoted at 14 to 2 per cent.a month. The thrifty Michael Reese is said to have half repented of a generous gift to the University of California, with the exclamation, ‘Ah, but I lose the interest,’ a very natural regret when interest was 24 per cent. perannum.”! After railway connection in 1869, Eastern loans began to flow in. The decade, 1870-1880, was one of transition during which the phenomenon of high interest was gradually replaced by the phenomenon of borrowing from outside. The rate of interest consequently dropped from 11 per cent. to 6

per cent.?

‘Since 1880 the economic history of California,

or at least of San Francisco and vicinity, has not differed so very much from that of the rest of the country.” * During recent years the rate on mortgages in San Francisco, up to the time of the earthquake and fire, has been 4 to 45 per cent. exclusive of the state tax. The same phenomena of enormous interest rates were also exemplified in Colorado and the Klondike. There were many instances in both these places during the transition period from poverty to affluence, when loans were contracted at over 50 per cent. per annum, and the borrowers regarded themselves as lucky to get rates so “low.”

It was also conspicuously true that the first buildings and apparatus constructed in these regions were very unsub1 Carl C. Plehn, ‘Notes concerning the Rates of Interest in California,” Quarterly Publications of the American Statistical Association, September, 1899, pp. 351-352. 3 Tbid., p. 353. 2 Tbid., p. 353.

THE

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stantial. Rude board cabins were put up in a day. Thus, high interest, borrowing, and unsubstantial capital were the phenomena which attended these communities when undergoing their rapid expansion. In Nevada in the seventies, when the mines were in-

creasing their product and the income of its inhabitants was tending upwards, the rate of interest was high and the people in debt. The bonded state debt itself amounted to $500,000 and drew 15 per cent. interest. In the next decade all these conditions were reversed. The mines were on the decline,? the rate of interest fell, and the state and territorial debts were largely paid off.* The fall of the rate of interest in this case could not have been due to the introduction of loans from outside, except so far as old debts were

refunded

at lower rates;

fresh loans were

seldom

made, as the state had ceased to be a good place for new investments. In the last few years new Nevada mines in the gold-field region have been opened. Loans are again entering the state, and the same cycle of history as above described is about to be repeated. Lumbering communities often go through a somewhat similar cycle. The virgin forests when first attacked tend to increase rapidly the income-streams of those who exploit them. Then comes a period of decrease. Thus in Michigan two or three decades ago the lumber companies found a profitable investment, and borrowed in order to exploit the Michigan forests. After the exploitation was complete and the forests had been (often unwisely) exhausted, those regions ceased to be a desirable place for investment, and

their owners came into the position, not of receiving, but of seeking, investments. After the trunk lines of railway were completed, connecting the Mississippi Valley with the East, there arose a great demand for loans to exploit the rich farming lands in that * See “Message of the Governor of the State of Nevada,” 1879. ? Mines and Quarries, 1902. Special Report U.S. Census, p. 255. * See later, “ Messages of the Governor of the State of Nevada.’’

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The rate of interest frequently was

10 and 12 per cent., and even higher.

During much of this

time the Northwestern Mutual Life Insurance Company, up to 1880, made an average rate on all its mortgage loans, $10,000,000 in amount, of nearly 10 per cent. Another striking proof of the demand for loans in the Middle West is shown in the experience of the New York and Connecticut life insurance companies. New York, up to 1880, had a law prohibiting the life insurance companies in that state from loaning on real estate outside of New York. Connecticut had no restriction in this regard, and her companies loaned extensively in the West. The

result is seen in the rates of interest realized on mortgage loans of companies in the two states. Taking the period 1860 to 1880 as a whole, the Connecticut companies realized 1,2, per cent. more than did the New York companies. Since 1880, the Middle West has developed rapidly, and

loans on farming lands are now made at low rates. During the past two years, certain of the insurance companies have been making mortgage loans in Illinois at 43 per cent.’ A similar history has recently been enacting itself in the northwest region of the United States. During the period of exploitation while the Great Northern and other railways were developing this territory, the phenomena of high interest and borrowing were almost universal. But latterly, much to the surprise of many Hasterners, it has been found that the rates of interest in these states have been at times lower even than in most American cities, and that the inhabitants have actually been seeking to lend to the East instead of to borrow from it.

§ 11 Australia furnishes another example of a country which, through improvement in the means of transportation, 1See Zartman, The Investments New York (Holt), 1906, pp. 89-91.

of Life

Insurance

Companies,

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[Cuar. XV

created = great demand for loans. The rate during the fifties on safe securities was rather low. This rate increased until, during the seventies, 7, 8, and 9 per cent. were usual. Since 1880 the rates have declined.’ England may perhaps be cited as exemplifying the same

phenomena which we have seen in the case of Nevada, though in a less degree. Thus, as Nevada has exhausted its mines of precious metals, so England is on the road toward exhaustion of its coal and iron supplies. This fact has been noted with considerable alarm by many economists, especially Jevons. It does not necessarily indicate that the economic power of Englishmen will be greatly or even at all lessened. Its significance shows itself in the tendency of England to become an investing country. It is the part of those who have property in mines not to use all of the product as income, but to reinvest in order to

maintain the capital. This the Englishmen have done and are doing; and being unable to make satisfactory investments at home, they have placed their loans all over the world. The income-stream produced for them by their native island is destined, perhaps, to decline, certainly not greatly to increase; but by saving from this declining income and investing in South America, Australia, South Africa, and other regions where the natural resources are on

the increase instead of on the wane, the Englishmen may still maintain their capital intact or even increase it. It is said, with how much accuracy I do not know, that Englishmen own an area in the United States as large as

Jreland.

The figures given by Giffen show that the na-

tional income increased for several decades, but that the

rate of increase slackened? for the decade 1875-1885 compared with 1865-1875; that whereas in the earlier decades there was a general increase in all directions, in the later * Zartman, The Investments of Life Insurance Companies, p. 103. ? Giffen, Growth of Capital, London (Bell), 1889. See also articles by Giffen in continuation of the same subject in Journal of Royal Statistical Society.

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decade there were many items of decrease,’ the most nota-

ble being of mines and ironworks;

? and finally, that among

the greatest increases was that of foreign investments.° We thus see that the rate of preference for present over

future goods, in its various manifestations —such as a high or low rate of interest, more or less lending and accumulation of capital, and the character of the instruments formed — depends upon the time-shape of the income-stream of a community, as determined by its natural resources; that in virgin countries like the United States in the last two centuries, Australia and South Africa, rich in timber, untouched ore, and raw materials

generally, the income-

stream is of the ascending type and produces a high rate of preference, whereas in older countries like England and Holland, in which the natural resources have been fully developed, and are even declining, the rate of preference tends to be low; such a country either uses up its income and thereby reduces its capital, or seeks economic salvation in foreign investment. § 12 The time-shape of an income-stream is, however, deter-

mined in part by other causes than natural resources. Among these causes, misfortune holds a high place in causing temporary depressions in the income-stream, that is, giving to it a time-shape which is first descending and afterwards ascending. The effect of such temporary depression is to produce a high valuation of immediate income during the depression period as compared with the valuation of the income expected after the depression is over. It isa matter of common observation in private life that loans often find their source in personal misfortune. The above-mentioned investigation of the conditions of borrowing among the poor‘ shows that the chief causes 8 Ibid., pp. 40-42. 2 Ibid., p. 35. 1 Ibid., p. 44. «U.S. Bureau of Labor Bulletin, No. 64, May, 1906, pp. 622 ff.

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[Cuapr. XV

for borrowing are a death or birth in the family, or protracted illness, the expense of which, even when amounting to only $10 or $20, would, without serious inroads on the daily necessities.

the loan, make

We may see the operation of the same principle on a larger scale in the case of the San Francisco earthquake, which, had it not been for the succor rendered by the whole country, would have cut down the income-stream of the city to the starvation point. In addition to the aid of many millions of dollars of gifts, there were needed also heavy loans. Whether these loans were used to produce sustenance, which is direct income, or to offset the cost of rebuilding the city, which is outgo, the effect is the same, —they were for the purpose of salving over a temporary injury to the income-stream. The effect on the rate of interest was slight, because of the opportunity to borrow heavily from outside. Had the city not had this opportunity, the depression in its income-stream could not have been mitigated, and the rate of interest would inevitably have

risen to a level comparable with that which prevailed in the same region a half century ago during the gold fever. In much the same way is the income-stream of a nation affected by war. The effects in this case, however, are more complex, owing, first, to the element of uncertainty which the war introduces until peace is declared; and, secondly, to the fact that wars are apt to be more protracted than most other misfortunes. The effect, according to previous explanations, should be that at the beginning

of the war the rates of interest on risky loans would be high. This would be especially true of the loans the periods of which are short, or not long enough to outlast the war. On the other hand, the rate of interest on safe loans would be lowered for short-term loans, and raised for long-term loans. A short-term loan relates to a descent in the income curve if repayable at a time when the income-stream is apt to be still further reduced. This descent in the income-stream,

together with the element of uncertainty, tends, as has been

Sec.12]

INDUCTIVE

VERIFICATION

(ECONOMIC)

seen, to lower the rate of interest on safe loans.

313

On the

other hand, for long-term loans intended to outlast the war, the rate of interest is apt to be high, for the income-

stream at the time of repayment may be expected to exceed the income-stream at the time of contract. At the close of the war, after peace is declared and the element of uncertainty introduced by it has disappeared, the rate of interest, even on short-term loans, will be high; for then the country is, as it were, beginning anew, and the same causes operate to make interest high as apply in the case of all new countries. The situation at this period is exemplified by the recent peace loan for Japan.

When the effects of the war include the issue of depreciated paper money, the rate of interest is affected in a somewhat more complex manner, being then subject to the influence of depreciation, according to the princi-

ples explained in Chapter V, and statistically verified in Chapter XIV. Among the most powerful causes which affect the timeshape of income-streams has been noted the effect of invention. That the claims which have been made for the effect of invention are verified in fact can scarcely be doubted when we consider the history of railway transportation. The very fact that during the last half century the chief outlet for investors’ savings has been in the creation of new railways, is sufficient testimony. What is true in the case

of this single invention or group of inventions is more signally true when a large number of inventions is being made. The effect of the activity of the inventive faculty must have materially contributed to keep up the rate of interest in the United States, and during the last generation in Germany. The striking way in which the rate of interest in Germany

has been maintained during the past century is shown by the experience of the Gotha Mutual Life Insurance Company,

the largest in Germany. From 1829 to 1838, this company made an average rate of 3.9 per cent. During the years

314

THE

RATE

OF INTEREST

[Cuar. XV

1850-1852, the rate realized was 3.9 per cent. In 1874, the rate had risen to 4.8, influenced partly by the same causes that had affected the interest rate all over the world, and partly by the great industrial progress which Germany was making. In 1885, the rate had fallen to 4.2 per cent., and in 1902 to 3.9 per cent., a rate the same as that which had been realized three quarters of a century before! *

§ 13 We have considered the effect on the rate of preference of those changes in the income-stream due to the growth or waning of natural resources and to the temporary influence of misfortunes and inventions. There remain to be considered those regular changes in the income-stream of a rhythmic or seasonal character. Though most persons are not aware of the fact, it can scarcely be doubted that the annual succession of seasons produces an annual cycle in the income-stream of the community. This is especially true of agriculture. Grains, fruits, vegetables, cotton, wool, and almost all the organic products flow from the earth at an uneven rate, and require for their production also an uneven expenditure of labor from man during different seasons of the year. Statistics of consumption show that the income enjoyed conforms in general to a cycle. Food products are usually made available in the warm months when crops ripen; logs are hauled out of the woods in winter, floated to mills in spring, and made into lumber in summer. But the tendency to a cycle is modified by the existence of stocks of commodities to tide over the periods of scarcity. The ice of winter is stored for summer, and the fruits of summer are canned and preserved for winter. Only so

far as such storage and preservation are difficult and expensive, or impair the quality of the goods thus held over,

or, because of the perishable nature of the goods, are im*See Zartman, pp. 105-106.

The

Investments

of Life Insurance

Companies,

Sec. 13]

INDUCTIVE

VERIFICATION

(ECONOMIC)

315

practicable, does there remain any cyclic change in enjoyed income. The cycle is different for different industries and for different classes of the population. The farmer is perhaps the most typical for the country as a whole. For him the lowest ebb is in the fall, when gathering and marketing his crops cause him a sudden expenditure of labor, or of money for the labor of others. To tide him over this period he may need to borrow. A whole group of other industries, particularly those connected with transporta-

tion, experience a sympathetic fluctuation in the incomestream. In the parlance of Wall Street, “money is needed to move the crops.” The rate of interest tends upward, as the following table shows :'— MONTHLY 60 TO

DISCOUNT RATES FOR PRIME TWO-NAME 90 DAYS’ PAPER IN NEW YORK CITY (Average for 10 years, 1896-1905) January . 4 8 - . 43 Kebruaryeveary fii Gt arias oa 4k (Marche amen erica. yc MRL ectete tc, |4.4 ADE Pee arene. ies €:, ifs ft 44 May ge maine? Bir meis teons achieve pe Sak JUNC e ect kk a me, We eroeo UL Vian Ue geh n aes IA CIGAd Gc tote fa Pe AUSUSES “rip ic. teshis) ths is is faked September. - 0. 2. ew 2 52 Coiear Ss alee oe A a ate ue INOVEIR Dei ae. fou. facet Mao « be SO Precentbenong.0 oases a pecan

pe: a”' + Tate

7

a

APPENDICES APPENDIX

TO CHAPTER

APPENDIX

TO CHAPTER

APPENDIX

TO CHAPTER

APPENDIX

To CHAPTER

APPENDIX

TO CHAPTER

APPENDIX

TO CHAPTER

APPENDIX

TO CHAPTER

b8 i IV. ¥. VIL. Vor NEE. XIV.

Propvuctiviry B6uM-BAWERK’s

APPRECIATION

THEORIES THEORY

AND

INTEREST

First APPROXIMATION SEconp THIRD

APPROXIMATION APPROXIMATION

STATISTICS

.

a

ee

oe

~~

et

ee ~

AOIOK aga exianen'l erwieeduess

Wien MTER, ayn"?

:

oe

fe.

a

OY exriiat) Wa

“wets? ‘aero Lett. recnaral ada waren

v.

7T Acta - on >

F awreiant) =.

ai¥ sainaulor

2

OTS eERCMTA |

350

APPENDIX

TO CHAPTER

II

which, since the first term is zero, represents the entire value of the m machines. The result is now independent of n. If m =10, this expression becomes 55a. The value of such a plant is then fifty-five times the annual yield of each machine. If this yield is $100, its value is $5500, which agrees with the calculation in the text.

APPENDIX

TO

CHAPTER

Bé6uM-BAWERK’s

IV

THEORY

§1 (ro Cu. IV, § 2) Nature of Various

Means — Arithmetical,

Geometrical, Harmonical, etc.

In general, a mean, @, of a number of magnitudes, a}, ay, ds, etc., is defined by an equation connecting these magnitudes and @ in such a manner that if all of the magnitudes, a,, a2, a3, ete. are equal to each other, the value of @ given by the equation will be equal to each of them. That this concept applies to the arithmetical, geometrical, and harmonical means is evident. These means may be defined by the following formule, where, for convenience, the number of elements, Q, My, etc., averaged is restricted to three. This restriction,

which may be very readily removed, is adopted brevity.

solely for

(1) Arithmetical, G+G+G=qt+u+a, orga Bets (2) Geometrical,

ee Or d= V/a, Az As

5 G3 1 Ag 1

(3) Harmonical,

pe

3 GQ

A

ds

The weighted arithmetical mean is given by the formula = = = = Wy + Woy + Ws Wh a+wa+ + Wet + waWs =w 1A,+ w Wg + AN, W3Mls OF Tp w, +0, + wy,

where the “weights” are the coefficients w,, w,, w;. This is the mean employed by Boéhm-Bawerk in the example given, the elements averaged, a, a2, a3, etc., being the different ages of the labor, 10 years, 9 years, 8 years, 7 years, etc., and the weights being the amount of labor, $20, $20, $5, $5, etc. The formule for both the geometrical and the harmonical averages may also be modified by introducing “ weights.” 351

APPENDIX

352

By

the

varying

infinite number

formula

may

we

of new kinds

defines

evidently Thus

of means.

Se

‘+i

IV

CHAPTER

TO

invent an the formula

ee eee

va “tT + Va,

@ as a sort of mean,

though

a complicated

(and

unsymmetrical) one, of a, a, ds.

§ 2 (ro Cu. IV, § 2) Case Illustrating Futility of Measuring Average Production Period.

Bohm-Bawerk’s chosen concept, which was doubtless adopted purely for convenience, that a given application of labor will yield its return in a single sum all at once, is far too simple to cover the facts as actually found. On the contrary, both the labor of forming instruments and their return are spread over a considerable period of time. This distribution in time may take any form, and some of its forms would render useless the simple arrangement of Bohm-Bawerk of production periods into a series of varying duration. Suppose, to take an extreme case, that a particular application of labor issues in two items of income, namely: $5 ten years after date, and $100 one hundred years after date; while another application of labor issues in only a single item worth $15 in twenty-five years. In this case it becomes impossible to call one of the production periods longer than the other; for whereas the second is definitely 25 years long, the first may be measured as any period between 10 and 100 years, according to the method employed for averaging 10 and 100. Moreover, it is not true that one of the alternatives will be chosen if the rate of interest is high, and the other if the rate of interest is low, as would be the case if they were subject to BéhmBawerk’s series. The application of labor which issued in the $5 and $100 would, oddly enough, be the most economical

if the rate of interest were either very high or very low, whereas the other alternative would be chosen in case the interest were

at a more

moderate

rate.

Thus, if the rate of

interest were 5%, the present value of the $15 due in 25 years would be $4.43, and that of the two items, $5 in 10 years and $100 in 100 years, would be $3.83. On the other hand, if the rate of interest were 1 %, the value of the $5 and $100 alternative would be $11.70 and of the $15 alternative $41.28.

BOHM-BAWERK’S

THEORY

353

Again, if the rate of interest were 25%, the value of the $5 and $100 would be $0.06 and of the $15 alternative, $0.54.

Hence,

if the rate of interest is 5%, the $15 alternative will be prefer-

able, whereas if the rate of interest is either 1% or 25%, the other alternative will be chosen. § 3 (to Cu. IV, § 3) Showing

how

Periods

of Production which are Relatively Unproductive are Eliminated.

Long but

That long processes (assuming their length to be measurable) are more productive than short processes is, as BohmBawerk says, a general fact, not a necessary truth. The reason lies in selection. It is not true that, of all possible productive processes, the longest are the most productive; but it is true that, of all productive processes actually employed, the longest are also the most productive. No one will select a long way unless it is at the same time a better way. All the long but unproductive processes are weeded out. The following illustration will make the process clear: Suppose that by means of 100 days’ labor invested to-day we can obtain a product of 100 units one year hence, or of 250 two years hence, of 50 three years hence, of 300 four years hence, of 250 five years hence, of 320 six years hence, of 100 seven years hence, of 300 eight years hence, etc.,—a series which we take quite at random. Out of this series of choices there will be eliminated those of 3, 5, 7, and 8 years, for each of these is outclassed by preceding choices. Thus, the 5-year period yielding 250 will be overshadowed by the 4-year period yielding 300; for this prospective return, being not only larger but earlier, will have a higher present value. Eliminating, then, these ineligible cases, we have left, to choose from, the 1, 2, 4, and 6 year periods. Of these, that one will be chosen of which the return will have the highest present value; and the present value will depend on the rate

of interest. If interest is at 5%, it will be profitable to invest the 100 days’ labor so as to mature in four years. AB is the discounted value of 300 at 5% for four years, it being found by the discount-curve BC drawn at 5% from C. Since this curve passes above the tops, C’, C", C'"", of all the other vertical lines, this present value (at 5%) of 300 in four years

will be the maximum of the present values of all the returns, 2a

354

APPENDIX

TO CHAPTER

IV

100, 250, 50, etc. But if the rate of interest sinks to 2%, as indicated by the discount-curve B'C’, the point of maximum return is shifted forward to six years; for the discount-curve B'C' at 2% drawn through C" now passes above the tops (C, Cc", C'"", ete.) of all other lines, hence a six-year period will be chosen. If, on the other hand, the rate of interest were 10%, a similar construction would show that the two-year period would be selected, as the highest discount-curve would then pass through C". But inno case will the highest discount curve touch the top of one of the short lines, 100, 50, 250, 100.

Fia. 25.

§ 4 (ro Cu. IV, § 4) Mathematical

Refutation

of Béhm-Bawerk’s

Claim

as

to

Ground

of

Preference for Present over Future Investment of Labor.

Let the products obtainable by processes of 1, 2, 3, ete. years be pj, ps, ps, etc., and the “marginal utilities reduced in perspective” beginning in 1888 be w, ws, us, etc. Then, A

MONTH’S

LABOR

In 1888 YIELDS

For the

economic | Units of period

product

1585 1889

P1 De

1890 1891

Ds ps

etc.

etc,

In 1889 yIELDS

Marginal ;

|Amount of

utility

value of

reduced

entire

in persp.

product

U1

a

ie uy

AVAILABLE

Piva ‘oats

Ole vin etc.

wee

= ou

ad at

BOHM-BAWERK’S

THEORY

355

We shall show that the labor available in 1888 is more valuable than that in 1889, provided only u, > w,> us, > Ww, ete. ; that is, that the maximum of the first series of puw’s, relating to 1888, is greater than the maximum of the second series, relating to 1889 (assuming of course that maxima exist). To prove this, select the maximum of the second series. Suppose it to be p,w, This is necessarily less than p,u; in the first series; for since u.< us by hypothesis, it follows that Psa < p33 That is, there necessarily exists in the first series a term greater than the greatest term in the second series. A fortiori must the greatest term in the first series exceed the greatest in the second series. In other words, the value for 1888 exceeds that for 1889, provided only the marginal utilities descend, whether or not the productivities ascend.

APPENDIX

TO

APPRECIATION

CHAPTER AND

V

INTEREST

§ 1 (ro Cu. V, § 2) History of Theory of Appreciation and Interest

Investigation shows that the present writer was by no means the first to conceive the relation between appreciation and interest. Apparently the earliest was the anonymous author’ of a remarkable pamphlet entitled: ‘A Discourse Concerning the Currencies of the British Plantations in America,” Boston, 1740 (reprinted in the Economic Studies of American Economic Association, 1897). He writes :— “© The Arguments

current amongst the Populace in favour of Paper

Money, are,

‘¢T, alleged Interest that in Use of

In most of the Paper Money Colonies one of the principal Reasons for their first Emissions ; was, to prevent Usurers imposing high upon Borrowers, from the Scarcity of Silver Money. It is true, all Countries the increased Quantity of Silver, falls the Interest or Money; but large Emissions of Paper Money does naturally rise

the Interest to make good the sinking Principal:

for Instance, in the

Autumn, A. 1737, Silver was at 26s. to 27s. per Ounce, but by a large Rhode Island Emission, it became in Autumn 1739, 29s. per Oz. this is 7 per Cent. Loss of Principal, therefore the Lender, to save his Principal from sinking, requires 13 per Cent. natural Interest (our legal Interest being 6 per Cent.) for that Year. In Autumn A. 1733, Silver was 22s. per Oz. by large Emissions it became 27s. in the Autumn, A. 17384; is 22 per Cent. loss of Principal ;and the Lender to save his Principal; requires 28 per Cent. natural Interest for that Year. Thus the larger the

Emissions, natural Interest becomes the higher ; therefore the Advocates for Paper Money (who are generally indigent Men, and Borrowers) ought

not to complain, when they hire Money at a dear nominal Rate. ‘‘Tf Bills were to depreciate after a certain Rate, Justice might be done

to both contracting Parties, by imposing the Loss which the Principal may sustain in any certain Space of Time (the Period of Payment), upon the Interest of a Bond or Price of Goods : but as Depreciations are uncertain, great Confusions in Dealings happen.”

1 Now identified as the physician, William Douglass.

356

APPRECIATION

AND

INTEREST

357

John Stuart Mill expressed the same view,! as have also Robert Goodbody,? Jacob de Haas,’ and Professor John B. Clark.* A principle which apparently has been independently discovered by each of these economic students and quite possibly by others,’ is likely to be of some importance. The present writer published in 1896 a monograph ® in which he worked out the relation between interest and appreciation in quantitative form, its application to special cases, its statistical verification, as well as its significance in the theory of interest and in the practical problem of regulating the standard of deferred payments. The major part of the material contained in this monograph is reproduced in Chapter V, Chapter XIV, and this Appendix. That the appreciation or depreciation of money does actually

1 Principles of Political Economy, Book 38, Ch. 23, § 4. [A single paragraph. ] 2Mr. Robert Goodbody, Broker, New York, has for years in his trade-letters maintained the doctrine that the rate of interest is high when money is depreciating, and low when money is appreciating. This he discovered about 1876, when the decline in silver was attracting attention. He was then much interested in the higher mathematics, and as he expressed it, ‘‘ accident or something caused me to differentiate the equation of imports and exports of any country, not with respect to time, but with respect to the variation of the standard of value. The result was that I found that the fraction formed by the ratio of call money as numerator and time money as denominator was smaller when the money standard was falling and larger when it was rising.”’ 8¢¢ A Third Element in the Rate of Interest,’’ Journal of the Royal Statistical

Society,

March,

1889.

[An

extended

discussion,

with

statistics.] 4¢¢The Gold Standard in the Light of Recent Theory,’’ Political Science Quarterly, September, 1895. [Applied to the bimetallic controversy.] 5 Mr. Byron W. Holt has cited other cases in which the relation between appreciation and interest has been recognized. In his paper entitled ‘‘ Interest and Appreciation ’’ (Sound Currency, Vol. V, No. 22,

1898) he mentions Senator Jones of Nevada, Professor T. N. Carver, now of Harvard, David I. Greene of Hartford, and Professor H. H. Powers, formerly of Leland Stanford. 6 «‘ Appreciation and Interest: a study of the influence of monetary appreciation and depreciation on the rate of interest, with applications to the bimetallic controversy and the theory of interest.” Publications of

the American 442.

Economic

Association, 1896,

Vol. XI, No. 4, pp. 331-

TO CHAPTER

APPENDIX

358

V

influece the rate of interest is now well recognized by those who have given attention to the subject.’ § 2 (ro Cu. V, § 3) Formula Connecting the Rates of Interest in two Diverging Standards.

In order to state the general relation between the rates of interest and appreciation or depreciation, let wheat fall in gold price (or gold rise in wheat price) so that the quantity of gold which would buy one bushel of wheat at the beginning of the year will buy 1+ a bushels at the end, a being therefore the rate of appreciation of gold in terms of wheat. Let the rate of interest in gold be 7, and in wheat be j, and let the principal of the loan be D dollars or its equivalent B bushels.

Our alternative contracts are then : — For D dollars borrowed, D+ Di or D(1 +7) dollars are due in 1 yr. For B bushels borrowed, B+ Bj or B(1+j) bushels are due in 1 yr.

and our problem is to find the relation between 7 and j, which

will make the D(1 +‘) dollars < the B(1 +) bushels.? At first, At the end of the year,

D D

dollars = B dollars = B(1 +a)

bu. bu.

Hence at theend of the year D (1+7)dollars = B(1 + a) (1+7)bu. Since D(1 +7) is the number of dollars necessary to liquidate the debt, its equivalent B(1 +a) (1+7%) is the number of bushels necessary to liquidate it. But we have already designated this number of bushels by B(1 +). 1See Professor Marshall’s testimony, Indian Currency Report, 1899, Pt. Il, p. 169; Graziani, Studi sulla teoria dell’ interresse, Turin, 1898, pp. 120-29; and Joseph F. Johnson, Money and Currency, Boston (Ginn),

1905, p. 158. But the subject has the business journals. See The Bond number of Moody’s Magazine, 1905, editorial on the effects of increasing

as yet attracted little attention in Record, April, 1896 ; also the first in which the ‘‘Symposium ’’ and the supply of gold are partly devoted to the relation between monetary depreciation and the rate of interest. The same material together with much else of importance is assembled in The Gold Supply and Prosperity, by Byron W. Holt, New York (Moody Publishing Co.), 1907. See also J. P. Norton, ‘‘The Depreciation of Gold,’”’ Yale Review, 1906-7, pp. 293-306. 2 The symbol = signifies ‘* equivalent to,”?

APPRECIATION

AND

INTEREST

359

Our result, therefore, is : — Dollars

Bushels

Bushels

at the end of one yearD (1+ i) B(1+/) = B(1+a) (1+), (1) which, after B is canceled, discloses the formula : —

1+j=(+a)d+%), or

J=

t+a+ia.

(2) (3)

or in words: The rate of interest in the relatively depreciating standard is equal to the sum of three terms, viz. the rate of interest in the appreciating standard, the rate of appreciation itself, and the product of these two elements. Thus, to offset the appreciation, the rate of interest must be lowered by slightly more than the rate of appreciation.!

We may introduce depreciation in a similar manner. Instead of saying gold appreciates at the rate a, relatively to wheat, we may say, wheat depreciates at the rate d, relatively to gold.? This means that wheat has sunk in terms of gold in the ratio 1 to 1—d, and reasoning similar to the foregoing shows that

1+i=(1—d)(+/)).

(4)

Equations (2) and (4) may be conveniently combined, thus :

iyi

wien ia

(5)

Since : + is the ratio of the value of gold at the end of the

year to its value at the beginning (all in terms of wheat), that is, the ratio of divergence of the two standards expressed in wheat, while

is the same ratio of divergence expressed

in gold, and since 1+7 is the “amount” of $1 put at interest for one year, while 1+/ is the “amount” of one bushel; we may state equation (5) as follows : — 1 Professor Clark (Political Science Quarterly, September, 1895) implies that 1% appreciation is offset by dess than 1% reduction of interest. But in making his calculation he has failed to ‘‘compound.”” The numerical illustrations of the eighteenth century pamphleteer (supra) are also

erroneous. £.g. instead of 28% the figure should be 29.32%. Professor Marshall (Principles of Economics, Vol. I, 3d ed., p. 674) gives a correct example, designed to show the losses from a fluctuating currency. 2 The relation between d and a is (1 + a) (1 — d) = 1, which is evident from equation (5), or may be easily shown independently.

360

APPENDIX

TO

CHAPTER

V

The ratio of divergence between the standards equals the ratio between their “ amounts.” This is, perhaps, the simplest mode of conceiving the relation, and stress is laid upon it, because it brings into prominence the “amount,” or ratio of future payment to present loan, a magnitude which in most questions of interest plays a more important réle than the rate of interest itself. Equation (5) gives the relation between i and j in terms of aord. From it follows the value of j in terms either of i and a or of ¢ and d, and also the value of ¢ in terms either of j and a or of j and d, thus: —

1+j

a

1+a

pstbos

|

1d

©)

whence

j=ita+ia =;+

(6)

or

i=j—d—ja

(7)

=1=*

It follows that j exceeds i by more than the rate of appreciation, which in turn is more than the rate of depreciation (i.e, j-—ti>a>d). § 3 (vo Cu. V, § 4) Formule,

when

Rates of Interest and of Appreciation are Reckoned oftener than Yearly.

In case we take the half-year instead of the year as the interval for compounding the rates of interest and of appreciation, it may readily be shown that the formula

1+j=(1+7%) (1+4) gives place to

Ag

pct

&

14 y=(145)(1+3) whence it also follows the relation

that instead of j=i+a-+ia,

we have

jeitat> In case the interest and appreciation are compounded quarterly, the formula becomes

jaitat+y,

APPRECIATION

AND

INTEREST

361

and soon. At the limit, when the rates of interest and appreciation are reckoned continuously, the last term vanishes and the formula becomes simply j =i+ a. § 4 (ro Cu. V, § 5) Case of Partial Payments.

First, consider the case in which no interest is paid until the end of the term of years. Let us suppose, for instance, a savings bank which receives $100, gold standard, and repays the depositor in five years at 5% compound interest. Let there be an alternative standard, say wheat, worth, at the beginning of the loan, $1 per bushel; but suppose that, in terms of wheat, gold is known to appreciate constantly by 1% per annum. What would be the rate of interest in terms of wheat? If the repayment were to be made in one year, the equivalent of the 5% would be a rate of interest in terms of wheat of 6, %, since the “amount” of a dollar of gold put at interest one year would be $1.05, and this would be worth, in bushels of wheat, 1.05 multiplied by 1.01, or 1.06, bushels. This result, 6,%, is as true for a series of years as for one year. This may be seen by separating the contract into several contracts of one year each. If we imagine deposited to-day in separate savings banks $100 in gold, and its equivalent, 100 bushels of wheat, they will amount in one year respectively to $1.05 at 5%, and its equivalent, 106.05 bushels at 6; %. We may now regard these equivalent amounts as withdrawn, but immediately redeposited for one year. Then, with the same rate of interest in gold and the same relative appreciation, we shall obtain the same rate of interest in wheat, so that $105 and its equivalent, 106.05 bushels, will amount in one year respectively to $110.25 at 5%, and its equivalent,

112.47 bushels at 61,%.

In this way each successive pair of

“amounts,” including the last, will be equivalent.

For simplicity we have considered only the case in which the debt is allowed to accumulate to the end. The most general case, however, is one in which the repayments are in installments,

Suppose, as before, that the interest in gold is

5% and that

gold is known to appreciate 1% per annum relatively to wheat. A farmer mortgages his land for $1000, or its then equivalent,

APPENDIX

362

TO

V

CHAPTER

1000 bushels of wheat, and agrees to pay annually the interest and such parts of the principal as he can save, making the repayment complete in seven years. Our problem is to find that rate of interest in wheat which will make the contracts in gold and wheat equivalent in every respect. The solution is precisely the same as before, viz. 6.5%. For, at the end of one year, the farmer’s debt amounts to $1050 or its then equivalent 1060.50 bushels. Let us suppose that he finds himself able to pay, not only the interest, $50, but also $50 of the “principal,” that is, $100 all together. The equivalent of this in wheat is 101 bushels. Hence he can either pay $100 on $1050.00 leaving $950.00 or 101 bu. on 1060.50 bu. leaving 959.50 bu. and, since the “amounts” $1050 and 1060.50 bu. are equivalent and the deductions $100 and 101 bu. are equivalent, the remainders $950 and 959.50 bu. must also be equivalent; in fact, this may be seen directly, since, with gold appreciating 1%, $950, originally worth 950 bu., becomes worth 1% more or 959.50 bu. Thus the farmer’s remaining debt at the end of the first year is the same whether measured in wheat or gold, and since the same reasoning applies to the second year, third year, etc., the equivalence remains to the end of the contract. It is worth noting here that the $100 payment in gold would be regarded as consisting of half “interest” and half “principal,” whereas the equivalent payment in wheat, 101 bu., will be regarded as 60.50 bu. “interest,” and 40.50 bu. “principal.” The liquidation of the contract during the seven years may thus be supposed to take place in either of the following equivalent ways: —

GOLD STANDARD (dollars) INTEREST

At beginning In 1 year In 2 years In 3 years In 4 years In 5 years In 6 years In 7 years SS

SS

AMOUNT

PAYMENT

50.00

1050.00

100.00

47.50 45.00

997.50 945.00 840-00 724,50 577.50 315.00

97.50 145.00 150.00 174.50 277.50 315.00

40.00 34.50 27.50 15.00

PRINCIPAL

REMAINING

1000.00 950.00 900.00 800.00 690.00 550.00 300.00 0.00

APPRECIATION WHEAT

AND

STANDARD

INTEREST (bushels) ee

At In In In In In In In

beginning 1 year 2 years 3 years 4 years 5 years 6 years 7 years

60.50 58.05 55.54 49.87 43.44 34.97 19.27

363

1060.50 1017.55 973.63 874.11 761.46 613.03 337.73

101.00 99.46 149.39 156.09 183.40 294.57 337.73

PRINCIPAL REMAINING

1000.00 959.50 918.09 824.24 718.02 578.06 318.46 0.00

In these two tables, every entry in one is equivalent to the corresponding entry in the other except those in the interest columns. We thus see that the farmer who contracts a mortgage in gold is, if the interest is properly adjusted, no worse and no better off than if his contract were made in a “wheat” standard. This principle, that debts in different standards are equivalent if the rates of interest in the two standards are properly adjusted, holds true, of course, no matter whether the “partial payments” are large, small, or none at all; no matter whether

the interest payments are made in full, in part, or not at all. The principals in the two standards are not equivalent, except at the beginning, nor are the annual interest sums equivalent; but the excess of the burden of interest in one

standard is accompanied by a deficiency in the burden of the principal, and vice versa. § 5 (to Cn. V, § 5) Formule for Cases of Compound Interest and Partial Payments.

The general case is precisely similar. If a debt in either of two alternative standards is to accumulate at compound interest, the rates of interest in the two standards must, in order that the contracts in each shall be equivalent, conform to the formula, 1+j=(1+

Remainder,

YEAR

Dollars

fBQ+/) =

Bushels

B (1+a) (1+)

fB(1+a) (142)

(1—/) D (1+?) =(1—/JS) B(14+j)= (1-S) B (1+a@) (142)

In like manner the unpaid remainder second year can be shown to be Dollars

at the end of the

Bushels

Cm fT) (17) Dl tee

(TT) Ga) Bae

=(1—-f!)

Bushels

A-f) BA +a) 1 +07,

and so on for any number of years. Each result again yields the formula (14+j)=(1+a) (1+7). Similar reasoning applied to each succeeding year yields the same formula. The case in which there are no partial payments is met by putting f, f', equal to zero.

APPRECIATION

AND

INTEREST

365

§ 6 (ro Cu. V. § 5) Case

of Separate Payments of Interest and Principal in one of the Two Standards and Equivalent Payments in the Other.

Suppose alternative contracts in gold at 5% and wheat at 635%, and suppose that the interest in the gold contract is annually paid and the principal redeemed in ten years. The following tables will show what are the equivalent operations in the wheat standard. LiquipaTIon IN GoLp STanparD, ConsisTInG OF ANNUAL INTEREST ($50) AND Fina Principat ($1000).

PAYMENT

At beginning (Dollars) In 1 year

50.00

— 1050.00

— 50.00

In 2 In 3 In 4 In 5 In 6 In 7 In 8 In 9 In 10

50-00 50.00 50.00 50.00 50.00 50.00 50.00 50.00 50-00

1050.00 1050.00 1050.00 1050.00 1050.00 1050.00 1050.00 1050.00 1050.00

50.00 50.00 50.00 50.00 50.00 50.00 50.00 50.00 1050.00

years years years years years years years years years

EquiIvALENT

LiquipaTION

IN

WHEAT

STANDARD;

INTEREST

At beginning (Bushels)

seeee

1000.00 1000.00 1000.00 1000.00 1000.00 1000.00 1000.00 1000.00 1000.00 1000.00 0.00

ANNUAL

ARE Less THAN INTEREST (60.50 Bu.) anp Finan THAN Principat (1000 Bu.).

PRINCIPAL REMAINING

PAYMENTS

Payment

PAYMENT

ie a

—

_—

In

1 year

60.50

1060.50

50.50

1010.00

In

2 years

61.10

1071.10

51.00

1020.10

In In In

38 years 4 years 5 years

61.72 62.32 62.96

1081.82 1092.62 1103.65

51.52 52.03 62.55

1030.30 1040.59 1051.00

In

6 years

63.59

1114.59

53.08

1061.51

years years years years

64.22 64.86 65.51 66.17

1125.73 1136.98 1148.35 1159.84

53.61 54.14 54.68 | 1159.84

1072.12 1082.84 1093.67 0.00

In 7 In 8 In 9 In 10

OOOO

—

More

1000.00

eooooouums.d

TO

APPENDIX

366

V

CHAPTER

If we suppose, conversely, that interest in the wheat standard is annually met and the principal redeemed in ten years, the equivalent operations in the gold standard will be as shown below. LiquipaTion

IN WHEAT

STANDARD,

(60.50 Bu.) anp Fina INTEREST

At In In In In In In In In

beginning (Bushels) 1 year 2 years 3 years 4 years 5 years 6 years 7 years

CONSISTING

Princrear

OF

ANNUAL

INTEREST

(1000 Bv.).

AnoueE

PAYMENT

sfeoe gosto

—

_

_

1000.00

60.50 60.50 60.50 60.50 60.50 60.50 60.50

1060.50 1060.50 1060.50 1060.50 1060.50 1060.50 1060.50

60.50 60.50 60.50 60.50 60.50 60.50 60.50

1000.00 1000.00 1000.00 1000.00 1000.00 1000.00 1000.00

8 years

60.50

1060.50

60.50

1000.00

In 9 years In 10 years

60.50 60.50

1060.50 1060.50

60.50 | 1060.50

1000.00 0.00

EquivaLent

LiquipaTION

IN

Gotp

ARE GREATER THAN INTEREST ‘THAN PRINCIPAL ($1000). INTEREST

At beginning (Dollars) year

In 1 In 2 In 3 In 4 In 6 In 6 In 7 In 8 In 9 In 10

years

years years years years years years years years

SranparpD;

($50)

anpD

saree

ANNUAL

Finat

PAYMENT

_~ 1050.00 1039.60 1029.30 1019.11 1009.02 999.03 989.19 979.39 969.69 960.08

PAYMENTS

Payment

Less

Gat

1000.00 990.10 980.29

970.58 960.97 . :

951.46 942.04 932.76 823.52 914.37 0.00

§ 7 (ro Cu. V, § 5) Case of Separate Payments of Interest and Principal in both Standards.

Let us next compare the liquidations in the two standards by the simple annual payment of interest in each (i.e, $50 in

APPRECIATION

AND

INTEREST

367

the gold standard and 60.50 bu. in the wheat standard, not inter-equivalent) and in ten years, final payment of principal ($1000 and 1000 bu. not inter-equivalent). In this case the individual payments in the two cases do not correspond, but the present values of the debts, reckoned at any date whatever, are always identical. Thus, the present value, at the date of contract, of the interest and principal, separately computed, at 6 % and 6,4 % in the two standards respectively, will be :1—

Present value of all interest payments, Present value of principal due in 10 years, Present value of total,

Dollars

Bushels

386.09 < 444.24 613.91 > 555.76 1000.00 = 1000.00

If the present values were computed five years after the date of the contract, and the “amounts” of past interest were computed for the same point of time, the items would be: — Dollars

Interest (present value and amounts), Principal (present value), Total, The two sums here, though not lent magnitudes; for whereas at 1 bushel of wheat were equivalent, nual appreciation of gold relatively

Bushels

492.75 < 595.88 783.53 > 745.50 1276.28 =< 1341.38

equal numbers, are equivathe outset $1 of gold and now, after five years of anto wheat at the rate of 1 %,

we shall find $1 worth (1.01)* bushels, or 1.051 bu., whence $1276.28 will be worth 1341.38 bushels. We thus see that it would be just as much of a hardship to pay the higher interest in wheat during the whole period as to pay the more onerous principal in gold at last.

§ 8 (ro Cu. V, § 5) Case of Perpetual Annuity.

The case of a perpetual annuity may be given special consid-

eration. As is well known, the present value of a perpetual annuity is its “capitalized” value. Thus, if the rate of interest is taken at 5 %, the present value of a perpetual annuity of $50 per annum is $1000.

Applying the same principle to the

1 The symbol < is here used for ‘‘ is less than the equivalent of,” and > for ‘‘ is more than the equivalent of.’’

APPENDIX

368

TO

CHAPTER

V

wheat annuity of 60.50 bushels and extending the previous reasoning, we find that the two annuities are equivalent. At first sight this seems impossible, since 6,1; % is a higher rate of interest than 5%. This is true, numerically, and it is also true that the early payments of 60.50 bushels are actually more valuable than $50. But after a certain time (in this particular case 19 years) the reverse is true. The 19th payment of $50 in gold is worth 60.40 bushels, while the 20th is worth 61.01 bushels. That is, the recipient of the wheat annuity has at first a slight advantage over the recipient of the gold annuity, which ceases and becomes a slight disadvantage after 19 years. To derive the formula for the time at which the relative values of the two annuities become reversed, let the rate of interest in gold be i, in wheat j; let the two annuities be Di and Bj, their capitalized values being D and B, (D=B at the beginning), and let x be the number of years in which Bj is as valuable as or more valuable than Di. Then Bushels Dollars

At the end of x years,

Biz Di

At the end of «+1

Bj< Di

years,

and since we know that in x years D= B(1+ a)’, and hence Di = Bi(1 +a)"; and likewise inx +1 years, Di Bi(1 + a)? =; we see that the previous inequalities become :— Bushels

Bushels

At the end of « years,

Bj = Bid +a)?

At the end of x+1 years,

Bj < Bi(l+a)**?

which may be combined in the formula :— i(1+a)*